Difficult# Visualizing Vector Angles: Linear Combination

LINALG-ZBYEAV

Let $\boldsymbol{u}$ and $\boldsymbol{v}$ be nonzero vectors in $\mathbb{R}^n$, and let $k = \Vert \boldsymbol{u}\Vert$ and $\ell = \Vert\boldsymbol{v}\Vert$.

If the angle formed between $\boldsymbol{u}$ and $\boldsymbol{v}$ is $60^\circ$ and $w=\ell\boldsymbol{u} + k\boldsymbol{v}$, what is the angle formed between $\boldsymbol{u}$ and $\boldsymbol{w}$?