If a x b = 4i + 5j - 7k, find (a + b) x (a - b)

Question

I believe you solve this by using the distributive law for the cross/vector product.

So far I have,

$$(a \times a) + (a \times -b) + (b \times a) + (b \times -b)=0 + (a \times -b) + (b \times a) + 0$$

I'm not sure what else to do from here.

Would appreciate any help.

Thank you.

Answer 1

By antisymmetry, it's $-2a\times b=-8i-10j+14k$.

Answer 2

Hints. You can always factor out a scalar, so we have that $a×-b=-(a×b)=b×a.$ Thus, the result is $2(b×a),$ or $$-2(a×b).$$