272t1s08sol

# 272t1s08sol - Mat 272 Test 1 Dr. Firoz 1. Find the center...

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Mat 272 Test 1 Dr. Firoz 1 1. Find the center and radius of the sphere 2 2 2 4 4 4 8 16 1 0 x y z x y + + - + - = . Solution: Center at (1, -2, 0) and radius (3/ 2) 2 2. Given a vector 4,4,3 u =< > . Find a vector of magnitude 10 in the direction of the given vector. Solution: 10 4,4,3 41 v = < > 3. Find orthogonal projection of v i j k = + + onto 2 2 b i j = + and then find the vector component of v orthogonal to b . Remember 2 b v b proj v b b = and vector component of v orthogonal to b is b v proj v - Solution: 2 1,1,0 b v b proj v b b = =< > 4. Consider the function 2 2 2 4 1 z x y + = + . Draw the level curves for 1 x = . Clearly label the axes and the level curves. z For x = 1, 2 z y = ± y 5. Find a vector equation for the line through the point P(5, -2, -1) parallel to the vector 2,3,2 v =< - > Solution: 5 2 ,3 2,2 1 r t t t =< - - - > 6. Find the length of the curve ( ) 4 ,2sin ,2cos , 1 3 r t t t t t =< > - ≤ ≤ Solution: 3 1 2 5 8 5 L dt - = =

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Mat 272 Test 1 Dr. Firoz
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## This note was uploaded on 05/09/2008 for the course MAT 272 taught by Professor Firoz during the Spring '08 term at ASU.

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272t1s08sol - Mat 272 Test 1 Dr. Firoz 1. Find the center...

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