{"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":"42ac0fa8-0dc9-579a-ba08-801831b2aebd","task_key":"precalculus--test--42ac0fa8-0dc9-579a-ba08-801831b2aebd","task_revision_id":"1","upstream_id":"","short_description":"The line described by","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The line described by\\n\\\\[\\\\begin{pmatrix} 2 \\\\\\\\ -1 \\\\\\\\ 3 \\\\end{pmatrix} + t \\\\begin{pmatrix} k \\\\\\\\ 2 \\\\\\\\ 1 \\\\end{pmatrix}\\\\]is perpendicular to the line described by\\n\\\\[\\\\begin{pmatrix} 2 \\\\\\\\ -1 \\\\\\\\ 1 \\\\end{pmatrix} + u \\\\begin{pmatrix} 2 \\\\\\\\ 1 \\\\\\\\ 2 \\\\end{pmatrix}\\\\]and passes through the point $(4,a,b).$  Find $a + b + k.$\",\"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":[]}