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Let $\mathbf{u}$ and $\mathbf{v}$ be nonzero vectors in 2 - or 3 -space, and let $k=\|\mathbf{u}\|$ and $l=\|\mathbf{v}\|$.

Prove that the vector $\mathbf{w}=l \mathbf{u}+k \mathbf{v}$ bisects the angle between $\mathbf{u}$ and $\mathbf{v}$.
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