samsoln23x1s10 - MATH 23 Sample First Exam was February...

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Unformatted text preview: MATH 23 Sample First Exam was: February, 2003 NAME : Dodson, B. Section 110-313 (Last, First) 1. (15 points ) If U, V and W are the vectors U = i- 3 j + k, V = 2 i- j + 3 k and W =- i + 2 j- k, where i, j and k are the unit vectors in the direction of the coordinate axes, find the following. (a) the dot product of U and V U · V = 2 + 3 + 3 = 8 . (b) the scalar projection of V onto W (= component of V in the direction of W ) comp W ( V ) = V · W | W | =- 2- 2- 3 √ 1+4+1 =- 7 √ 6 . (c) the vector projection of V onto W proj W ( V ) = comp W ( V ) u W =- 7 √ 6 1 √ 6 ‡- i + 2 j- k · =- 7 6 ‡- i + 2 j- k · , where u W is the unit vector in the direction of W . 2. (10 points ) Find the center and radius of the sphere with equation x 2- 6 x + y 2 + 2 y + z 2 = 3 . x 2- 6 x + 9 + y 2 + 2 y + 1 + z 2 = 3 + 9 + 1 , so ( x- 3) 2 + ( y + 1) 2 + z 2 = 13 , and center = (3, -1, 0), radius = √ 13 ....
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samsoln23x1s10 - MATH 23 Sample First Exam was February...

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