C3PracticeTest1Sol

C3PracticeTest1Sol - MA 242 Test 1 Solutions 1[5 points...

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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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C3PracticeTest1Sol - MA 242 Test 1 Solutions 1[5 points...

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