Chapter 2.4, Problem 194E

In the following exercises, vectors $\text{u}$ and $\text{v}$ are given. Find unit vector $\text{w}$ in the direction of the cross product vector $\text{u}\times \text{v}$ . Express your answer using standard unit vectors.

194. Show that $\text{u}\times \text{v}$ and $2\text{i}-14\text{j}+2\text{k}$ cannot be orthogonal for any a real number, where $\text{u}=\text{i}+7\text{j}-\text{k}$ and $\text{v}=\alpha \text{i}+5\text{j}+\text{k}.$