# tsl230 - Cross Product Between Vectors ^ ^ Consider two...

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Cross Product Between Vectors Consider two vectors ~ A = A x ˆ i + A y ˆ j + A z ˆ k and ~ B = B x ˆ i + B y ˆ j + B z ˆ k . ~ A × ~ B = AB sin φ ˆ n . ~ A × ~ B = - ~ B × ~ A . ~ A × ~ A = 0 . ~ A × ~ B = AB ˆ n if ~ A ~ B . ~ A × ~ B = 0 if ~ A k ~ B . ~ A × ~ B = ( A x ˆ i + A y ˆ j + A z ˆ k ) × ( B x ˆ i + B y ˆ j + B z ˆ k ) = A x B x ( ˆ i × ˆ i ) + A x B y ( ˆ i × ˆ j ) + A x B z ( ˆ i × ˆ k ) + A y B x ( ˆ j × ˆ i ) + A y B y ( ˆ j × ˆ j ) + A y B z ( ˆ j × ˆ k ) + A z B x ( ˆ k × ˆ i ) + A z B y ( ˆ k × ˆ j ) + A z B z ( ˆ k × ˆ k ) . Use ˆ i × ˆ i = ˆ j × ˆ j = ˆ k × ˆ k = 0 , ˆ i × ˆ j = ˆ k, ˆ j ×
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## This note was uploaded on 04/30/2008 for the course PHYS 204 taught by Professor Andrevantonder during the Spring '07 term at Rhode Island.

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