First slide

Vectors

Question

The unit vector parallel to the resultant of the vectors $\vec{A} = 4 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $\vec{B} = - \hat{i} + 3 \hat{j} - 8 \hat{k}$ is

Easy

A

$\frac{1}{7} (3 \hat{i} + 6 \hat{j} - 2 \hat{k})$
B

$\frac{1}{7} (3 \hat{i} + 6 \hat{j} + 2 \hat{k})$
C

$\frac{1}{49} (3 \hat{i} + 6 \hat{j} - 2 \hat{k})$
D

$\frac{1}{49} (3 \hat{i} - 6 \hat{j} + 2 \hat{k})$

Solution

Resultant of vectors $\vec{A} and \vec{B}$
$\vec{R} = \vec{A} + \vec{B} = 4 \hat{i} + 3 \hat{j} + 6 \hat{k} - \hat{i} + 3 \hat{j} - 8 \hat{k}$
$\vec{R} = 3 \hat{i} + 6 \hat{j} - 2 \hat{k}$
$\vec{R} = \frac{\vec{R}}{| \vec{R} |} = \frac{3 \hat{i} + 6 \hat{j} - 2 \hat{k}}{\sqrt{3^{2} + 6^{2} + {(- 2)}^{2}}} = \frac{3 \hat{i} + 6 \hat{j} - 2 \hat{k}}{7}$

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