Cross product: is this a valid operation
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Cross product: is this a valid operation

[From: ] [author: ] [Date: 11-05-11] [Hit: ]
-It may work in some cases but not always-Yes. its valid.......
I was wondering if it's valid to use a FOIL sort of approach to this cross product (a, b, c, n are vectors)

n = (a-b) x (b-c)
is it true then that
n = (a x b) - (a x c) - (b x b) + (b x c)
so then n = (a x b) + (b x c) + (c x a)?

thanks in advance

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Cross product is indeed distributive over addition. So FOIL approach is okay. Also cross product is anticommutative so that -(axc)=cxa is correct. So you expresssion for n is correct.

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It may work in some cases but not always

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Yes. it's valid.
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