Mathematics 1229A/B Midterm Oct,2010

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Use the following for questions 1, 2, 3 and 4. Let u = (2, 1, 2) and v = ( 2, 3, 6). [ 1 mark ] find 3u v. 3u v = 3(2, 1, 2) ( 2, 3, 6) = (6, 3, 6) ( 2, 3, 6) = (6 ( 2), 3 3, 6 6) = (8, 0, 12) [ 1 mark ] find u v. E: 8 u v = (2, 1, 2) ( 2, 3, 6) = 2( 2) + 1(3) + ( 2)(6) = 4 + 3 12 = 13. E: ( 4, 2, 8) u v = (2, 1, 2) ( 2, 3, 6) = (1(6) 3( 2), ( 2)( 2) 6(2), 2(3) ( 2)(1)) = (6+6, 4 12, 6+2) = (12, 8, 8) If w = (1, 1, 1), nd the volume of the parallelepiped with edges (i. e. determined by) u, v. Volume = | (u v) w |

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