Let \(u\) and \(v\) be two vectors in \(\mathbf{R}^{2}\) whose Euclidean norms…

Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy ‖$u$‖=2‖$v$‖. What is the value of $\alpha$ such that $w = u + \alpha v$ bisects the angle between $u$ and $v$?