Chapter 2.4, Problem 196E

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.

196. Show that $\text{v}\times \text{u}$ is orthogonal to $\left(\text{u}\cdot \text{v}\right)\left(\text{u}+\text{v}\right)+\text{u}$ , when; $\text{u}$ and $\text{v}$ are nonzero vectors.