{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":637,"title":"Volume of a Parallelepiped","description":"Calculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex.\r\n\r\nA cube is a special case of a Parallelepiped.\r\n\r\nvectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\r\n\r\nV=1;\r\n\r\nvectors=[2 0 0;0 2 0;1 0 1]; % 45 degree half height Parallelepiped\r\n\r\nV=4;\r\n\r\n","description_html":"\u003cp\u003eCalculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex.\u003c/p\u003e\u003cp\u003eA cube is a special case of a Parallelepiped.\u003c/p\u003e\u003cp\u003evectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\u003c/p\u003e\u003cp\u003eV=1;\u003c/p\u003e\u003cp\u003evectors=[2 0 0;0 2 0;1 0 1]; % 45 degree half height Parallelepiped\u003c/p\u003e\u003cp\u003eV=4;\u003c/p\u003e","function_template":"function V = Parallelepiped_volume(vectors)\r\n  V=0;\r\nend","test_suite":"%%\r\nvectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\r\nV=1;\r\nassert(isequal(Parallelepiped_volume(vectors),V))\r\n%%\r\nvectors=[2 0 0;0 2 0;0 0 2]; % 2x2x2 Cube\r\nV=8;\r\nassert(isequal(Parallelepiped_volume(vectors),V))\r\n%%\r\nvectors=[2 0 0;0 2 0;1 0 1]; % Slanted one side 45 degrees, half h\r\nV=4;\r\nassert(isequal(Parallelepiped_volume(vectors),V))\r\n%%\r\nvectors=[2^0.5 2^0.5 0;-2^0.5 2^0.5 0;0 0 2]; % Rot 45,\r\nV=8;\r\nassert(V-.001\u003cParallelepiped_volume(vectors) \u0026\u0026 Parallelepiped_volume(vectors)\u003cV+.001)\r\n%%\r\nvectors=[2^0.5 2^0.5 0;-2^0.5 2^0.5 0;0 1 1]; % Rot 45, Slant 45, h/2\r\nV=4;\r\nassert(V-.001\u003cParallelepiped_volume(vectors) \u0026\u0026 Parallelepiped_volume(vectors)\u003cV+.001)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":465,"test_suite_updated_at":"2012-04-29T18:51:39.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-04-29T18:07:38.000Z","updated_at":"2026-03-11T22:13:33.000Z","published_at":"2012-04-29T18:51:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA cube is a special case of a Parallelepiped.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV=1;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evectors=[2 0 0;0 2 0;1 0 1]; % 45 degree half height Parallelepiped\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV=4;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":637,"title":"Volume of a Parallelepiped","description":"Calculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex.\r\n\r\nA cube is a special case of a Parallelepiped.\r\n\r\nvectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\r\n\r\nV=1;\r\n\r\nvectors=[2 0 0;0 2 0;1 0 1]; % 45 degree half height Parallelepiped\r\n\r\nV=4;\r\n\r\n","description_html":"\u003cp\u003eCalculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex.\u003c/p\u003e\u003cp\u003eA cube is a special case of a Parallelepiped.\u003c/p\u003e\u003cp\u003evectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\u003c/p\u003e\u003cp\u003eV=1;\u003c/p\u003e\u003cp\u003evectors=[2 0 0;0 2 0;1 0 1]; % 45 degree half height Parallelepiped\u003c/p\u003e\u003cp\u003eV=4;\u003c/p\u003e","function_template":"function V = Parallelepiped_volume(vectors)\r\n  V=0;\r\nend","test_suite":"%%\r\nvectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\r\nV=1;\r\nassert(isequal(Parallelepiped_volume(vectors),V))\r\n%%\r\nvectors=[2 0 0;0 2 0;0 0 2]; % 2x2x2 Cube\r\nV=8;\r\nassert(isequal(Parallelepiped_volume(vectors),V))\r\n%%\r\nvectors=[2 0 0;0 2 0;1 0 1]; % Slanted one side 45 degrees, half h\r\nV=4;\r\nassert(isequal(Parallelepiped_volume(vectors),V))\r\n%%\r\nvectors=[2^0.5 2^0.5 0;-2^0.5 2^0.5 0;0 0 2]; % Rot 45,\r\nV=8;\r\nassert(V-.001\u003cParallelepiped_volume(vectors) \u0026\u0026 Parallelepiped_volume(vectors)\u003cV+.001)\r\n%%\r\nvectors=[2^0.5 2^0.5 0;-2^0.5 2^0.5 0;0 1 1]; % Rot 45, Slant 45, h/2\r\nV=4;\r\nassert(V-.001\u003cParallelepiped_volume(vectors) \u0026\u0026 Parallelepiped_volume(vectors)\u003cV+.001)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":465,"test_suite_updated_at":"2012-04-29T18:51:39.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-04-29T18:07:38.000Z","updated_at":"2026-03-11T22:13:33.000Z","published_at":"2012-04-29T18:51:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA cube is a special case of a Parallelepiped.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evectors=[1 0 0;0 1 0;0 0 1]; % Unity Cube\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV=1;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evectors=[2 0 0;0 2 0;1 0 1]; % 45 degree half height Parallelepiped\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV=4;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[{"value":"Computational Geometry I","count":1,"selected":false}],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"vector operators dot cross\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}