Find $\mathbf u\cdot\mathbf v$ and hence determine the angle between $\mathbf u$ and $\mathbf v$ in degrees correct to three significant figures.

The vector $\mathbf w=\mathbf u+k\mathbf v$ where $k\in\mathbb R$ Determine the value of $k$ for which $\mathbf w$ is perpendicular to $\mathbf u$