QTA_MAT 2030_11SS

# QTA_MAT 2030_11SS - ANSWERS TO QUIZZES TESTS AND FINAL MAT...

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XIAOLONG HAN Abstract. This is the collection of answers to the questions on quizzes, tests and ﬁnal. If you ﬁnd any mistake, please notify me. Quiz 1 (1) a + b = h 2 , - 18 i (2) 2 a + 3 b = h 1 , - 42 i (3) | a | = 13 (4) | a - b | = 10 Quiz 2 (1) u and v are orthogonal. (2) The triangle is right-angled, and PQR is the right angle. Test 1 (1) The three points do not lie on a straight line. (2) v = h 2 , 2 3 i . (3) ± 1 17 ( i + 4 j ) or ±h 17 17 , 4 17 17 i . (4) ( orth a b ) · a = ( b - proj a ) b = b · a - ( proj a b ) · a = b · a - a · b | a | 2 a · a = b · a - a · b | a | 2 | a | 2 = b · a - a · b = 0. (5) arccos( 3 3 ). (6) a × b = 15 i - 3 j + 3 k . (7) Parametric equations: x = 2+ t , y = 1 - t , z = t . Symmetric equations: x - 2 = y - 1 - 1 = z or x - 2 = 1 - y = z . Additional : Parametric equations: x = t , y = 1, z = - t . Symmetric equations: x = - z , y = 1. Quiz 3

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QTA_MAT 2030_11SS - ANSWERS TO QUIZZES TESTS AND FINAL MAT...

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