Question

Prove that \( (\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})=2(\vec{b} \times \vec{a}) \)

Answer 1

\((\vec a + \vec b) \times (\vec a - \vec b)\)

\(= \vec a \times \vec a - \vec a \times \vec b + \vec b \times \vec a - \vec b \times \vec b\)

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

\(= 2 (\vec b \times \vec a)\)