{"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":"2432e50e-4c9b-5ee5-9908-51213a4d29fd","task_key":"precalculus--test--2432e50e-4c9b-5ee5-9908-51213a4d29fd","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{a},$ $\\mathbf{b},$ $\\mathbf{c}$ be three vectors such that…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $\\\\mathbf{a},$ $\\\\mathbf{b},$ $\\\\mathbf{c}$ be three vectors such that $\\\\|\\\\mathbf{a}\\\\| = \\\\frac{1}{\\\\sqrt{2}},$ $\\\\|\\\\mathbf{b}\\\\| = \\\\frac{1}{\\\\sqrt{3}},$ $\\\\|\\\\mathbf{c}\\\\| = \\\\frac{1}{\\\\sqrt{6}},$ $\\\\|\\\\mathbf{a} + \\\\mathbf{b} + \\\\mathbf{c}\\\\| = 1,$ and\\n\\\\[\\\\mathbf{a} = k (\\\\mathbf{b} \\\\times \\\\mathbf{c})\\\\]for some scalar $k.$  Find the angle between $\\\\mathbf{b}$ and $\\\\mathbf{c},$ in degrees.\",\"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":[]}