# Quiz1 - -2 u + 3 v . Answer:-2 u + 3 v =-12 i-4 j + 10 k...

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Name: MTH 234 Section 60 Answers to Quiz 1, January 18, 2011 1. (6 points) Consider the points P 1 (2 , - 3 , 5) and P 2 (4 , - 1 , - 3). (a) Find the distance between P 1 and P 2 . Answer: | P 1 P 2 | = p 2 2 + 2 2 + ( - 8) 2 = 72 (b) Find the midpoint of the line segment P 1 P 2 . Answer: (3,-2,1) (c) Find the equation of the sphere with center P 1 going through P 2 . Answer: ( x - 2) 2 + ( y + 3) 2 + ( z - 5) 2 = 72 2. (7 points) Consider the vectors u = i - j + 4 k and v = - 2 i - 2 j + 6 k . (a) Find the vector
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Unformatted text preview: -2 u + 3 v . Answer:-2 u + 3 v =-12 i-4 j + 10 k (b) Find proj v u . Answer: proj v u =-6+2+24 4+4+36 (-2 i-2 j + 6 k ) = 10 11 (-i-j + 3 k ) (c) Find two orthogonal vectors a and b such that a + b = u and a has the same direction as v . Answer: a = proj v u = 10 11 (-i-j + 3k ) , b = u-a = 1 11 (43 i-j + 14 k )...
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## This note was uploaded on 02/03/2012 for the course MTH 234 taught by Professor Irinakadyrova during the Summer '10 term at Michigan State University.

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