What is the relationship of $\bfa \times \bfb$ and $\bfb \times \bfa$? Prove it using components.
Solution
Whatever the relationship is, we will need a proof in terms of components. Hence, we write $\bfa \times \bfb$ and $\bfb \times \bfa$ in terms of the components of $\bfa$ and $\bfb$.
Let $\bfa = \langle a_1, a_2, a_3 \rangle.$ Let $\bfb = \langle b_1, b_2, b_3 \rangle.$