sample1_soln_p1

sample1_soln_p1 - TAM 210/211 BL1 Sample Exam1 Name:...

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TAM 210/211 BL1 Name: Sample Exam1 Section: 1. For the three vectors j i A ˆ 4 ˆ 3 + = v , k j i B ˆ ˆ ˆ + + = v , and k C ˆ 5 = v find each of the following: a. B A v v + k j i k j i B A ˆ ˆ 5 ˆ 4 ˆ ˆ ) 1 4 ( ˆ ) 1 3 ( + + = + + + + = + v v b. B A v v k j i k j i B A ˆ ˆ 3 ˆ 2 ˆ ) 1 0 ( ˆ ) 1 4 ( ˆ ) 1 3 ( + = + + = v v c. B A v v 7 4 3 0 1 1 4 1 3 = + = + + = B A v v d. C A v v × j i k j i k j i C A ˆ 15 20 ˆ 0 0 4 3 ˆ 5 0 0 3 ˆ 5 0 0 4 5 0 0 0 4 3 ˆ ˆ ˆ = + = = × v v You can also do this without determinates using the distributive property: ( ) i j k j k i k j i C A 20 ˆ 15 ˆ 5 ˆ 4 ˆ 5 ˆ 3 ˆ 5 ˆ 4 ˆ 3 + = × + × = × + = × v v e. ( ) C B A v v v × × There is a short way and a long way (the latter involving solving two cross products). The short way: ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) k j i j i k k j i k j i B A C C A B ˆ ˆ ˆ ˆ 4 ˆ 3 ˆ 5 ˆ 5 ˆ 4 ˆ 3 ˆ ˆ ˆ + + + + + + = v v v v v v ( ) () ( ) k k k j i ˆ 35 1 4 1 3 ˆ 5 0 ˆ ˆ ˆ = + + + =
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