Chapter 2.4, Problem 193E

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.

193. Determine the real number $\alpha$ such that $\text{u}\times \text{v}$ and $\text{i}$ are orthogonal, where $\text{u}=3\text{i}+\text{j}-5\text{k}$ and

$\text{v}=4\text{i}-2\text{j}+\alpha \text{k}$ .