Question

A unit vector parallel to the resultant of the vectors

$\overrightarrow{ A }=4 \hat{ i }+3 \hat{ j }+6 \hat{ k }$ and $\overrightarrow{ B }=-\hat{ i }+8 \hat{ j }-8 \hat{ k }$

• A. $\frac{3 \hat{i}+11 \hat{j}-2 \hat{ k }}{2}$
• B. $\frac{\hat{ i }+2 \hat{ j }-3 \hat{ k }}{\sqrt{166}}$
• C. $\frac{3 \hat{i}+11 \hat{j}-2 \hat{k}}{\sqrt{134}}$
• D. $\frac{4 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{11}}$

Answer 1

Answer: (C)

Resultant of vectors $\overrightarrow{ A }$ and $\overrightarrow{ B }$
So, $\overrightarrow{ R }=\overrightarrow{ A }+\overrightarrow{ B }$
$\overrightarrow{ R }=4 \hat{ i }+3 \hat{ j }+6 \hat{ k }-\hat{ i }+8 \hat{ j }-8 \hat{ k }$
$\overrightarrow{ R }=3 \hat{ i }+11 \hat{ j }-2 \hat{ k }$
$\vec{R}=\frac{3 \hat{i}+11 \hat{j}-2 \hat{k}}{\sqrt{(3)^{2}+(11)^{2}+(-2)^{2}}}$
$\vec{R}=\frac{3 \hat{i}+11 \hat{j}-2 \hat{k}}{\sqrt{9+121+4}}=\frac{3 \hat{i}+11 \hat{j}-2 \hat{k}}{\sqrt{134}}$