2010 Algebra Test 2

2010 Algebra Test 2 - 1. Math1151 Algebra. S1 2010 Test 2....

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Unformatted text preview: 1. Math1151 Algebra. S1 2010 Test 2. Version 2a. (1) Is the vector u = (1 ,- 5 ,- 2) T parallel to the plane x = (2 , 4 ,- 1) T + v + w where v = (1 , 2 , 2) T and w = (3 ,- 1 , 7) T ? Solution. The vector u is parallel to the plane above if u span { v,w } , that is, if there exists , such that v = v + w . Putting into matrix form and row reducing gives 1 3 | 1 2- 1 | - 5 2 7 | - 2 - 1 3 | 1- 7 | - 7 1 | - 4 - 1 3 | 1- 7 | - 7 | - 5 so u = v + w have no solutions. Hence u 6 span { v,w } . (2) Compute D = 1 3- 1 2 1- 1 5 7 Solution. D = 1(7)- 3(14)- (10 + 1) =- 46 (3) Find the shortest distance from the point with coordinate vector a = (3 ,- 1 , 4) T to the plane with equation x + 3 y + 3 z = 5. Solution. We first pick a point b = (- 1 , 1 , 1) on and note that n = (1 , 3 , 3) is normal to the . The shortest distance from a to is given by a- b = (4 ,- 2 , 3) d = | proj n ( a- b ) | = | ( a- b ) n |...
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2010 Algebra Test 2 - 1. Math1151 Algebra. S1 2010 Test 2....

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