{"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":"eee2f297-b61a-5470-9228-9d60fa28dfd3","task_key":"precalculus--test--eee2f297-b61a-5470-9228-9d60fa28dfd3","task_revision_id":"1","upstream_id":"","short_description":"The matrix for projecting onto a certain line $\\ell,$ which passes through the…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"The matrix for projecting onto a certain line $\\\\ell,$ which passes through the origin, is given by\\n\\\\[\\\\begin{pmatrix} \\\\frac{1}{50} & \\\\frac{7}{50} \\\\\\\\ \\\\frac{7}{50} & \\\\frac{49}{50} \\\\end{pmatrix}.\\\\]Find the direction vector of line $\\\\ell.$  Enter your answer in the form $\\\\begin{pmatrix} a \\\\\\\\ b \\\\end{pmatrix},$ where $a,$ and $b$ are integers, $a > 0,$ and $\\\\gcd(|a|,|b|) = 1.$\",\"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":[]}