Exercise 23

In The Vector Nature of the Cross Product, we stated “Because the cross product works well with linear combinations, $\vu\times\vv$ is perpendicular to any linear combination of $\vu$ and $\vv$.” We want to verify this algebraically here. Specifically, show that $\vu\times\vv$ will be orthogonal to any vector of the form $a\vu+b\vv$.