{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"969f50d0-b6d0-5ba6-b11f-a63b2e0abc27","task_key":"precalculus--test--969f50d0-b6d0-5ba6-b11f-a63b2e0abc27","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{a} = \\begin{pmatrix} 2 \\\\ 0 \\\\ 1 \\end{pmatrix},$ $\\mathbf{b} =…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $\\\\mathbf{a} = \\\\begin{pmatrix} 2 \\\\\\\\ 0 \\\\\\\\ 1 \\\\end{pmatrix},$ $\\\\mathbf{b} = \\\\begin{pmatrix} 1 \\\\\\\\ 1 \\\\\\\\ 1 \\\\end{pmatrix},$ and $\\\\mathbf{c} = \\\\begin{pmatrix} 4 \\\\\\\\ - 3 \\\\\\\\ 7 \\\\end{pmatrix}.$  Find the vector $\\\\mathbf{v}$ such that $\\\\mathbf{v} \\\\times \\\\mathbf{b} = \\\\mathbf{c} \\\\times \\\\mathbf{b}$ and $\\\\mathbf{v} \\\\cdot \\\\mathbf{a} = 0.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}