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
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.