The unit vector parallel to the resultant of the vectors A→=4i^+3j^+6k^ and B→=−i^+3j^−8k^ is

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 $\vec{A}$ and $\vec{B} = \vec{A} + \vec{B}$

$\vec{A} + \vec{B} = 3 \hat{i} + 6 \hat{j} - 2 \hat{k}$

$∴$ Unit vector $= \frac{\vec{A} + \vec{B}}{| \vec{A} + \vec{B} |} = \frac{3 \hat{i} + 6 \hat{j} - 2 \hat{k}}{7}$

$\frac{1}{7} [3 \hat{i} + 6 \hat{j} - 2 \hat{k}]$

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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

Solution:

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