# MATH / 

task_id: b154a8a8-e3d0-5d2e-99de-809f8bf7c20c
task_key: precalculus--test--b154a8a8-e3d0-5d2e-99de-809f8bf7c20c
task_revision_id: 1

{"level":"Level 5","problem":"Let $\\mathbf{a} = \\begin{pmatrix} -2 \\\\ 5 \\end{pmatrix}$ and $\\mathbf{b} = \\begin{pmatrix} 1 \\\\ 3 \\end{pmatrix}.$  Find the vector $\\mathbf{c}$ so that $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}$ are collinear, and $\\mathbf{b}$ bisects the angle between $\\mathbf{a}$ and $\\mathbf{c}.$\n\n[asy]\nunitsize(0.5 cm);\n\npair A, B, C, O;\n\nA = (-2,5);\nB = (1,3);\nO = (0,0);\nC = extension(O, reflect(O,B)*(A), A, B);\n\ndraw(O--A,Arrow(6));\ndraw(O--B,Arrow(6));\ndraw(O--C,Arrow(6));\ndraw((-3,0)--(3,0));\ndraw((0,-1)--(0,6));\ndraw(interp(A,C,-0.1)--interp(A,C,1.1),dashed);\n\nlabel(\"$\\mathbf{a}$\", A, NE);\nlabel(\"$\\mathbf{b}$\", B, NE);\nlabel(\"$\\mathbf{c}$\", C, NE);\n[/asy]","type":"Precalculus"}

Source: https://github.com/hendrycks/math

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GET /api/v1/write?intent=publish&task_id=b154a8a8-e3d0-5d2e-99de-809f8bf7c20c&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}