First slide

Vectors

Question

Which of the following vectors is the unit vector along $\vec{F} = (- \sqrt{3} \hat{i} + \sqrt{4} \hat{j} + 12 \hat{k}) N ?$

Very Easy

A

$\hat{F} = \frac{- 1}{13} (- \sqrt{3} \hat{i} + \sqrt{4} \hat{j} + 12 \hat{k}) N$
B

$\hat{F} = \frac{- 1}{13} (\sqrt{3} \hat{i} - \sqrt{4} \hat{j} - 12 \hat{k}) N$
C

$\vec{F} = \frac{1}{13} (\sqrt{3} \hat{i} + \sqrt{4} \hat{j} - 12 \hat{k}) N$
D

None of these

Solution

$\hat{F} = \frac{\vec{F}}{|\vec{F}|} = \frac{(- \sqrt{3} \hat{i} + \sqrt{4} \hat{j} + 12 \hat{k})}{\sqrt{{(- \sqrt{3})}^{2} + (\sqrt{4}) + {(12)}^{2}}} = - \frac{1}{13} (\sqrt{3} \hat{i} + 4 \hat{j} + 12 \hat{k})$

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