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BAC-CAB_Rule

# BAC-CAB_Rule - DERIVATION OF BAC CAB RULE USING TERM BY...

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DERIVATION OF BAC - CAB RULE USING TERM BY TERM COMPONENT EXPANSION Use term - by - term expansion rather than summation notation to prove the following identity : (1) A â B â C = B A C - C A B ü Solution : The strategy here will be to write out the left hand side and right hand sides in term by term components and show they equal. Let' s start by noting explicitly that each of the vectors can be written in component form : A = A x x ` + A y y ` + A z z ` B = B x x ` + B y y ` + B z z ` C = C x x ` + C y y ` + C z z ` The right hand side of (1) becomes : (2) B A C - C A B = B x x ` + B y y ` + B z z ` A x C x + A y C y + A z C z - C x x ` + C y y ` + C z z ` A x B x + A y B y + A z B z = B x A x C x + B x A y C y + B x A z C z - C x A x B x - C x A y B y - C x A z B z x ` + B y A x C x + B y A y C y + B y A z C z - C y A x B x - C y A y B y - C y A z B z y ` + B z A x C x + B z A y C y + B z A z C z - C z A x B x - C z A y B y - C z A z B z z ` All the terms in eq. (2) are scalars, so the order of multiplication is irrelevant.

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BAC-CAB_Rule - DERIVATION OF BAC CAB RULE USING TERM BY...

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