HW1 - Physics 3122, Fall 2010: Homework Set 1 Solutions....

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Physics 3122, Fall 2010: Homework Set 1 Solutions. 1.5 r A × ( r B × r C ) [ ] z = A x ( r B × r C ) y A y ( r B × r C ) x = A x ( B z C x B x C z ) A y ( B y C z B z C y ) = ( A x B z C x A x B x C z ) ( A y B y C z A y B z C y ) + ( A z B z C z A z B z C z ) = ( A x C x + A y C y + A z C z ) B z ( A x B x + A y B y + A z B z ) C z = ( r A r C ) B z ( r A r B ) C z r A × ( r B × r C ) = ( r A r C ) r B ( r A r B ) r C 1.12 h = 10(2 xy 3 x 2 4 y 2 18 x + 28 y + 12 r h = 10(2 y 6 x 18)ˆ x + 10(2 x 8 y + 28)ˆ y r h = 0 6 x 2 y = 18 2 x 8 y = 28 x = 2 y = 3 h = 10( 12 12 36 + 36 + 84 + 12) = 720 x = 1 y = r h = 220ˆ x + y r h = r h / r h = ( ˆ x + ˆ y 1.20 (v) r × ( f r A ) = ( fA z ) y ( fA y ) z ˆ x + ( fA x ) z ( fA z ) x ˆ y + ( fA y ) x ( fA x ) y ˆ z = f A z y A y z ˆ x + f A x z A z x ˆ y + f A y x A x y ˆ z + A z f y A y f z ˆ x + A x f z A z f x ˆ y + A y f x A x f y ˆ z = f r × r A r A × v f 1.27 r × r f = ˆ x x + ˆ y y + ˆ z z × ˆ x f x + ˆ y f y + ˆ z f z =
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