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Classical Mechanics

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Moderate

Vector in the Unit Vector Notation

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Vector $\vec{u}$ is in the second quadrant and $\vec{u} \cdot \vec{u}=6$. The vector makes an angle of ${45}^{o}$ with respect to the negative x-axis.

Which of the following represents vector $\vec{u}$ written through unit vectors $\hat{i}$ and $\hat{j}$?

A

$3\hat{i} -3\hat{j}$

B

$-6 \hat{i} +6\hat{j}$

C

$-3\hat{i} + 3\hat{j}$

D

$\sqrt{3} \hat{i} -\sqrt{3} \hat{j}$

E

$-\sqrt{3} \hat{i} +\sqrt{3} \hat{j}$

F

$3\hat{i} + \sqrt{3}\hat{j}$