# Solution to #4-2

Paper 1 Difficulty:Medium

Let $\vec{u}=\begin{pmatrix} 3\\ k\\ -2 \end{pmatrix}$, and $\vec{v}=\begin{pmatrix} 5\\ -2\\ 7 \end{pmatrix}$, for $k>0$. The angle between $\vec{u}$ and $\vec{v}$ is $\frac{\pi }{2}$ radians.

Find the value of k.

[Maximum mark:5]