Question

Prove that ( vector a + vector b) * ( vector a - vector b) = a ^2 - b ^2?

Answer 1

Please see a Proof in Explanation.

Explanation:

Recall that the dot product of vectors is distributive and

commutative.

`:. (veca+vecb)*(veca-vecb)`,

`=veca*(veca-vecb)+vecb*(veca-vecb)`,

`=veca*veca-veca*vecb+vecb*veca-vecb*vecb`

`=veca^2-cancel(veca*vecb+veca*vecb)-vecb^2`, as desired!