messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 40
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n -1 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n\\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{a... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\rig... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n -1 ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\righ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n\\end{array}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{ar... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n\\end{arra... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n -1 \\\\\n\\end{arra... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n -1 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{ar... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 0 \\\\\n -1 \\\\\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{a... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{arr... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n -1 \\\\\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n\\e... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{a... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n -1 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n -... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n -1 \\\\\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{arr... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n -1 \\\\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n\\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{a... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n -1 ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\righ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n -1 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n\\end{array}\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n -1 \\\\\n -1 \\\\\n -1 \\\\\n\\end{arra... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{ar... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{a... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n -1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n ... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n 0 \\\\\n -1 \\\\\n 1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n\\... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 0 \\\\\n 1 \\\\\n -1 \\\\\n 1 \\\\\n 1 \\\\\n 1 \\\\\n 0 \\\\\n 0 \\\\\n\\en... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n 1 \\\\\n -1 \\\\\n 0 \\\\\n -1 \\\\\n 0 \\\\\n 0 \\\\\n\\end{array}\n\\right... | linear_algebra | vector_angles_and_projections |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "Find the angle between the following two vectors:\n$\\left(\n\\begin{array}{c}\n -1 \\\\\n 1 \\\\\n\\end{array}\n\\right)$ and\n$\\left(\n\\begin{array}{c}\n 1 \\\\\n... | linear_algebra | vector_angles_and_projections |
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