{"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":"9564f72c-6cce-5bdd-8d32-fbf5d7c8be77","task_key":"precalculus--test--9564f72c-6cce-5bdd-8d32-fbf5d7c8be77","task_revision_id":"1","upstream_id":"","short_description":"Let","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let\\n\\\\[\\\\mathbf{a} = \\\\begin{pmatrix} 5 \\\\\\\\ -3 \\\\\\\\ -4 \\\\end{pmatrix} \\\\quad \\\\text{and} \\\\quad \\\\mathbf{b} = \\\\begin{pmatrix} -11 \\\\\\\\ 1 \\\\\\\\ 28 \\\\end{pmatrix}.\\\\]There exist vectors $\\\\mathbf{p}$ and $\\\\mathbf{d}$ such that the line containing $\\\\mathbf{a}$ and $\\\\mathbf{b}$ can be expressed in the form\\n\\\\[\\\\mathbf{v} = \\\\mathbf{p} + \\\\mathbf{d} t.\\\\]Furthermore, for a certain choice of $\\\\mathbf{d}$, it is the case that for all points $\\\\mathbf{v}$ lying on the same side of $\\\\mathbf{a}$ that $\\\\mathbf{b}$ lies on, the distance between $\\\\mathbf{v}$ and $\\\\mathbf{a}$ is $t$.  Find $\\\\mathbf{d}$.\",\"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":[]}