{"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":"0ad049cc-044c-5531-ad50-9de02a7d3d3d","task_key":"precalculus--test--0ad049cc-044c-5531-ad50-9de02a7d3d3d","task_revision_id":"1","upstream_id":"","short_description":"A plane contains the vector $\\begin{pmatrix} 1 \\\\ 2 \\\\ 3 \\end{pmatrix}$ and has…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"A plane contains the vector $\\\\begin{pmatrix} 1 \\\\\\\\ 2 \\\\\\\\ 3 \\\\end{pmatrix}$ and has normal vector $\\\\begin{pmatrix} 4 \\\\\\\\ 5 \\\\\\\\ 6 \\\\end{pmatrix}.$  A line contains the vector $\\\\begin{pmatrix} -1 \\\\\\\\ 0 \\\\\\\\ 5 \\\\end{pmatrix}$ and has direction vector $\\\\begin{pmatrix} -1 \\\\\\\\ -1 \\\\\\\\ 2 \\\\end{pmatrix}.$  Find the point of intersection of the plane and line.\",\"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":[]}