First slide

Vectors

Question

Unit vector parallel to the resultant of vectors $\vec{A} = 4 \hat{i} - 3 \hat{j}$ and $\vec{B} = 8 \hat{i} + 8 \hat{j}$ will be

Moderate

A

$\frac{24 \hat{i} + 5 \hat{j}}{13}$
B

$\frac{12 \hat{i} + 5 \hat{j}}{13}$
C

$\frac{6 \hat{i} + 5 \hat{j}}{13}$
D

None of these

Solution

Resultant of vectors $\vec{A} and \vec{B}$
$\vec{R} = \vec{A} + \vec{B} = 4 \hat{i} - 3 \hat{j} + 8 \hat{i} + 8 \hat{j} = 12 \hat{i} + 5 \hat{j}$
$\vec{R} = \frac{\vec{R}}{| R |} = \frac{12 \hat{i} + 5 \hat{j}}{\sqrt{{(12)}^{2} + {(5)}^{2}}} = \frac{12 \hat{i} + 5 \hat{j}}{13}$

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