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Unformatted text preview: 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 x y z x y + + + = . Solution: 2 2 2 2 2 2 4( 2 8 ) 1 ( 1) ( 4) 21/ 4 x y z x y x y z + + + = + + + = The center is at (1, 4, 0) and radius 21/ 2 2. Given a vector 4,4,3 r =< > . Find a vector of magnitude 10 in the direction of the given vector. Solution: Unit vector along 4,4,3 41 u < > = , vector with magnitude 10 is 40,40,30 10 41 v u < > = = 3. Find the scalar and vector projection of the vector 5,0,5 a =<  > onto 5,2, 1 b =<  > Solution: Scalar projection of a onto b is 20 30 b a b comp a b = = and vector projection of a onto b is 2 20 5,2, 1 30 b a b proj a b b = = <  > Where 25 0 5 20 25 4 1 30 a b and b = +  = = + + = 4. Find orthogonal projection of 5, 6, 6 b =<    > onto 1, 4,8 a =< > The orthogonal projection of b onto a is 29 5, 6, 6 1, 4,8 81 a a orth b b proj b =  =<    > + < > 5. Find the area of the parallelogram with vertices P(0, 0, 0), Q(5, 1, 3), R(5, 0, 1)...
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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.
 Spring '08
 Firoz

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