Math206Test1

Math206Test1 - Mid-term Exam # 1 September 24, 2007 MthSc...

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Mid-term Exam # 1 September 24, 2007 MthSc 206 – 013: Calculus of Several Variables Instruction: PRINT your name clearly in capitals and underline your last name . NAME: EXAM SOLUTION 1. (3pts). Show that the following equation represents a sphere and find its center and radius: x 2 + y 2 + z 2 + 2 x - 6 y + 4 z + 10 = 0 . Solution: x 2 + 2 x + y 2 - 6 y + z 2 + 4 z = - 10 x 2 + 2 x + 1 + y 2 - 6 y + 9 + z 2 + 4 z + 4 = - 10 + 1 + 9 + 4 ( x + 1) 2 + ( y - 3) 2 + ( z + 2) 2 = 4 It is an equation for a sphere. The center is c ( - 1 , 3 , - 2) and its radius is 2 . 2. (8pts) Two vectors a = h 1 , 2 , 3 i and b = h 0 , 1 , 0 i are given. (a) (3pts) Find the scalar projection (scalar component) of b onto a . Solution: Comp a b = a b | a | = h 1 , 2 , 3 i ◦ h 0 , 1 , 0 i q (1) 2 + ( 2) 2 + ( 3) 2 = 2 6 = 3 3 = 0 . 577 . (b) (3pts) Find the vector projection of b onto a . Solution:
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This note was uploaded on 04/03/2008 for the course MTHSC 206 taught by Professor Chung during the Spring '07 term at Clemson.

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Math206Test1 - Mid-term Exam # 1 September 24, 2007 MthSc...

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