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Linear Algebra

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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 $\boldsymbol{w}$?

A

$120^\circ$

B

$90^\circ$

C

$60^\circ$

D

$45^\circ$

E

$30^\circ$

F

$15^\circ$