{"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":"89df67e5-96a2-525f-b05e-e48e2305b432","task_key":"precalculus--test--89df67e5-96a2-525f-b05e-e48e2305b432","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{w} = \\begin{pmatrix} 1 \\\\ 0 \\\\ -3 \\end{pmatrix}.$ The set of…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Let $\\\\mathbf{w} = \\\\begin{pmatrix} 1 \\\\\\\\ 0 \\\\\\\\ -3 \\\\end{pmatrix}.$  The set of vectors $\\\\mathbf{v}$ such that\\n\\\\[\\\\operatorname{proj}_{\\\\mathbf{w}} \\\\mathbf{v} = \\\\mathbf{0}\\\\]lie on a plane.  Enter the equation of this plane in the form\\n\\\\[Ax + By + Cz + D = 0,\\\\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\\\\gcd(|A|,|B|,|C|,|D|) = 1.$\",\"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":[]}