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

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Unformatted text preview: 1. Math1151 Algebra Test 1. S1 2010. Version 1a. (1) If A = (3 ,- 1 , 6) and B = (4 , 2 ,- 1). Find the distance from A to B and a unit vector u in the direction from A to B . Solution. The vector AB = (1 , 3 ,- 7) has length | AB | = 59, so the unit vector u parallel to AB is AB/ 59. Comments. A unit vector means a vector with length equal to one. For any vector b the vector b/ | b | is a unit vector parallel to b . (2) Are the lines x = (1 , 5 ,- 7) + (3 ,- 2 , 4) and x- 3 6 = 2 y + 5- 4 = z + 1 8 parallel? Solution. We first convert the Cartesian equations into parametric form: ` ( ) = 3- 5 / 2- 1 + 6- 2 8 The vectors (6 ,- 2 , 8) and (3 ,- 2 , 4) are clearly not multiples of each other, hence the lines are not parallel. (3) Find a parametric vector form of the plane with Cartesian equation 11 x 1- x 2- 3 x 3 = 5. Solution. Let a = (0 ,- 2 ,- 1), b = (1 , , 2) and c = (1 , 6 , 0) be three points on the plane. Then P ( , ) = a +...
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2010 Algebra Test 1 - 1. Math1151 Algebra Test 1. S1 2010....

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