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Unformatted text preview: MA 242 Test 1 Solutions 1. [5 points] Find an equation of the sphere with center (2,6,4) and radius 5. Solution: The equation of a sphere with center ( h, k, l ) and radius r is ( x h ) 2 +( y k ) 2 +( z l ) 2 = r 2 , so the equation of our sphere is ( x 2) 2 +( y +6) 2 +( z 4) 2 = 25 2. [5 points] What is the magnitude and direction of the zero vector? Solution: The zero vector is the only vector with magnitude 0 and no direction. 3. [20 points] Given the vectors→ a = < 5 , 4 , 2 > and→ b = < 2 , 2 , 1 > , compute the following: a) 2→ a + 3→ b b) → b  c)→ a •→ b d)→ a ×→ b e)→ b ×→ a f) Are the vectors→ a and→ b parallel, orthogonal or neither? Give a reason for your conclusion. Solution: a) 2→ a + 3→ b = 2 < 5 , 4 , 2 > +3 < 2 , 2 , 1 > = < 10 , 8 , 4 > + < 6 , 6 , 3 > = < 16 , 2 , 1 > b) → b  = p 2 2 + 2 2 + ( 1) 2 = √ 9 = 3 c)→ a •→ b = (5)(2) + ( 4)(2) + (2)( 1) = 0 d)→ a ×→ b = ˆ i ˆ j ˆ k...
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This note was uploaded on 03/31/2009 for the course MA 242 taught by Professor Bliss during the Spring '08 term at N.C. State.
 Spring '08
 Bliss

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