tsl229 - Dot Product Between Vectors ^ ^ Consider two...

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Dot 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 cos φ = AB A = BA B . ~ A · ~ B = ~ B · ~ A . ~ A · ~ B = AB if ~ A k ~ B . ~ A · ~ B = 0 if ~ A ~ 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
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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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