Math206Test2

Math206Test2 - Mid-term Exam # 2 October 17, 2007 MthSc 206...

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Unformatted text preview: Mid-term Exam # 2 October 17, 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). Find an equation of the plane that passes through P (- 1 , 1 , 1), Q (1 ,- 1 , 1), and R (1 , 1 ,- 1). Solution: First, we need to find a vector perpendicular to the plane that passes through the above three points. Let a =--→ P Q and b =-→ P R . Then we have a = h 2 ,- 2 , i and b = h 2 , ,- 2 i . Then n = a × b is perpendicular to the plane. Using these, we have n = a × b = ˛ ˛ ˛ ˛ ˛ ˛ i j k 2- 2 2- 2 ˛ ˛ ˛ ˛ ˛ ˛ = 4 i- (- 4) j + 4 k = 4 i + 4 j + 4 k = h 4 , 4 , 4 i . Let r be the position vector of P . Then we have r = h- 1 , 1 , 1 i . Hence an equation of the plane is 4( x + 1) + 4( y- 1) + 4( z- 1) = 0 x + y + z = 1 . 2. (2pts) Find the distance from the point (3 , 8 , 5) to the plane x- 2 y- 2 z = 1. Solution: D = | ax 1 + by 1 + cz 1 + d | √ a 2 + b 2 + c 2 = | 1 · 3 + (- 2) · 8 + (- 2) · 5 + (- 1) | p 1...
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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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Math206Test2 - Mid-term Exam # 2 October 17, 2007 MthSc 206...

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