23_Quiz1Solutions - =-18 √ 14 proj a b = a • b | a | 2...

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Math 23 - Quiz 1 September 13, 2007 Solutions 1. Determine whether the vectors a = < 6 , 4 , - 2 > and b = < - 2 , - 6 , 3 > are orthogonal, parallel, or neither. Solution: a b = - 12 - 24 - 6 = 0, so a and b are not orthogonal. a × b = 0, so a and b are not parallel. Therefore, neither. 2. Find the scalar and vector projections of b = < 1 , 6 , - 2 > onto a = < 2 , - 3 , 1 > . Solution: comp a b = a b | a | = 2 - 18 - 2
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Unformatted text preview: =-18 √ 14 proj a b = a • b | a | 2 a =-18 14 < 2 ,-3 , 1 > = <-18 / 7 , 27 / 9 ,-9 / 7 > 3. Find a vector orthogonal to the plane through the points P (2 , ,-3), Q (3 , 1 , 0), R (5 , 2 , 2). Solution: PQ = < 1 , 1 , 3 > and PR = < 3 , 2 , 5 > PQ × PR = <-1 , 4 ,-1 >...
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