Assignment 1 Solutions.- Vector Problems

# Assignment 1 Solutions.- Vector Problems - Assignment1...

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Assignment 1. Solutions Given: Determine: ( , ), ( , ) Solution: ( ) ( ) ( ) cos sin ( rr z xx r yy r xr r z r yr vv v v vvv θθ θ =++ == =⋅ = ⋅ + =− ve e k iv ie ik jv j )()( ) sin cos rz r +⋅ + =+ ej k j r e e 1. 2. Relations are correct i

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Assignment 1 (Cont) 1/2 2 2 2 1/2 1/2 (a) 2( ) 2( ) 2((2 3 ) (2 3 )) 8 6 8 (b) | | ( ) ( ) (64 36 64) =2 41 (c) (2 3 ) (2 3 + ) 4 3 7 (d) = (2 3 ) (2 3 xx yy zz DDD =+ = + + + = + + =⋅ = + + = + =⋅= + + = + = + × ++ DA B B A ik ij k i jk DD D EA B i k i j k FA B i k i j k 1/2 1/2 )6 2 6 - 9 9 4 6 () (e) (2 3 ) ( 2 ) 2 4 3 3 3 7 2 (9 49 4) (62) 1 ( 3 7 2 ) 62 = −+ = =− + + × × ×= + × + = ++−= ×=+ + = =− + kjj i k AC e AC i k i j k k j j i k ei j k 3.
Assignment 1 (Cont) 1/2 ( ) P ( ) () ( 9 4 6 ) 1 ( 9 4 6 ) (81 16 36) 133 11 7 ( 9 4 6 ) ( 2 ) 133 133 17 20 177 67 ( 2 ) (9 4 6 ) 133 133 133 133 e C =+ = ⋅+ =−⋅ ×− + + ≡= = = + + ×+ + ⋅= −+ + = + + = + Ce P e C e P C e AB F i j k ei j k eC i j k i j k Pi jk i i j k 3.(f) Cn Cp C n A B

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Assignment 1 (Cont) 4(a). () = = xyz y xz yy zx y z AAA xy z A AA z xx z z A A yz ⎛⎞ ∂∂ ∇⋅ = + + + + = ⎜⎟ ⎝⎠ =++ ∂∂∂ ∇× = + + × + + = =− −+ + Ai j k i j k j k i j k kjkiji i y x
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Assignment 1 Solutions.- Vector Problems - Assignment1...

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