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Multivariable Calculus

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Moderate

Component Form

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Let:

$$||{\bf u}|| =6$$
$$||{\bf u} + {\bf v}||=6\cdot \sqrt{2}$$

...and let's assume that ${\bf u}$ makes an angle of $45 ^{\circ}$ with a positive $x$-axis, while ${\bf u} + {\bf v}$ makes an angle of $90 ^{\circ}$ with the positive $x$-axis.

What is the component form of ${\bf v}$?

A

$\langle 3\sqrt{2},-3\sqrt{2} \rangle$

B

$\langle -3\sqrt{2},-3\sqrt{2} \rangle$

C

$ \langle -3\sqrt{2},-3\sqrt{2} \rangle$

D

$\langle -3\sqrt{2},3\sqrt{2} \rangle$

E

$\langle -6,0 \rangle$