HW16_1 - Prof. I. Biaggio Solutions HW 16 Physics 90, Fall...

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Prof. I. Biaggio Solutions HW 16 Physics 90, Fall 2006 1-4 Solutions Homework 16 35 This is just to train the use of the vector-product rules. There is not much to explain, but make sure you know these rules! Picture the Problem The cross product of the vectors j i A ˆ ˆ y x A A + = ! and j i B ˆ ˆ y x B B + = ! is given by ( ) ( ) ( ) ( ) j j i j j i i i B A ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ! + ! + ! + ! = ! y y x y y x x x B A B A B A B A ! ! ( ) () ( ) ( ) 0 ˆ ˆ 0 y y x y y x x x B A B A B A B A + ! + + = k k () ( ) k k ˆ ˆ ! + = x y y x B A B A ( a ) Find A ! × B ! for A ! = 4 i ˆ and B ! = 6 i ˆ + j ˆ 6 : ( ) ( ) ( ) ( ) k k j i i i j i i B A ˆ 24 ˆ 24 0 24 ˆ ˆ 24 ˆ ˆ 24 ˆ 6 ˆ 6 ˆ 4 = + = ! + ! = + ! = ! ! ! ( b ) Find A ! × B ! for A ! = 4 i ˆ and B ! = 6 i ˆ + 6 k ˆ : ( ) ( ) ( ) ( ) ( ) j j k i i i k i i B A ˆ 24 ˆ 24 0 24 ˆ ˆ 24 ˆ ˆ 24 ˆ 6 ˆ 6 ˆ 4 ! = ! + = " + " = + " = " ! ! ( c ) Find A ! × B ! for A ! = 2 i ˆ + j ˆ 3 and B ! =3 i ˆ + j ˆ 2 : ( ) ( ) ( ) ( ) ( ) ( ) ( ) () ( ) ( ) k k k j j i j j i i i j i j i B A ˆ 5 0 6 ˆ 9 ˆ 4 0 6 ˆ ˆ 6 ˆ ˆ 9 ˆ ˆ 4 ˆ ˆ 6 ˆ 2 ˆ 3 ˆ 3 ˆ 2 ! = + ! + + = " + " + " + " = + " + = " ! !
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Prof. I. Biaggio Solutions HW 16 Physics 90, Fall 2006 2-4 37 •• This is again vector-product training, but it also introduces a nice way of using vector products to
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HW16_1 - Prof. I. Biaggio Solutions HW 16 Physics 90, Fall...

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