I need to prove that (a – b) x (a + b) = 2(a x b), where a and b are both vectors. I can’t figure out a proof.?
I need to prove that ((a - b) \times (a + b) = 2(a \times b)), where (a) and (b) are both vectors. I'm struggling to find a proof for this equation. Can anyone help me understand how to approach this?
2 Answers
Ok, here’s how you do it. You know that
(a-b)x(a+b)= axa + axb – bxa – bxb
you know too that
axa = 0 and bxb = 0
you know too that
-bxa=axb then
(a-b)x(a+b) = axb +axb = 2(axb)
hope this helps.
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