ch03-p057 - 57. The three vectors are i j d1 = 3.0 + 3.0 +...

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57. The three vectors are 1 2 3 ˆˆ ˆ 3.0i 3.0 j 2.0k ˆˆˆ 2.0i 4.0 j 2.0k 2.0i 3.0 j 1.0k. d d d =− + + + =++ G G G (a) Since 23 ˆ 0i 1.0 j 3.0k dd +=− + GG , we have 12 3 2 ˆ ( ) ( 3.0i 3.0 j 2.0k) (0i 1.0 j 3.0k) 0 3.0 +6.0 3.0 m . dd d ⋅+= + + ⋅− + = G (b) Using Eq. 3-30, we obtain 10i 6.0 j 2.0k. ×= + + Thus, 123 3 ˆ ˆ ( ) ( 3.0i 3.0 j 2.0k) ( 10i 6.0 j 2.0k) 30 18 4.0 52 m .
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