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Parallelogram Law: Linear Combination with Three Vectors

LINALG-BBP51N

The vectors $\boldsymbol{u}$, $\boldsymbol{v}$, and $\boldsymbol{w}$ are vectors in $\mathbb{R}^2$ as illustrated below (the diagram is drawn to scale).

Express the unlabeled vector as a linear combinations of $\boldsymbol{u}$, $\boldsymbol{v}$, and $\boldsymbol{w}$.

A

$-\boldsymbol{u} + \boldsymbol{v} + \boldsymbol{w}$

B

$\boldsymbol{u} + \boldsymbol{v} - \boldsymbol{w}$

C

$\boldsymbol{u} - \boldsymbol{v} - \boldsymbol{w}$

D

$-\boldsymbol{u} + \boldsymbol{v} - \boldsymbol{w}$

E

$\boldsymbol{u} + \boldsymbol{v} + \boldsymbol{w}$

F

$\boldsymbol{u} - \boldsymbol{v} + \boldsymbol{w}$

G

$-\boldsymbol{u} - \boldsymbol{v} + \boldsymbol{w}$

H

$-\boldsymbol{u} - \boldsymbol{v} - \boldsymbol{w}$