Question

If $\overrightarrow{A}=4\hat{i}-2\hat{j}+6\hat{k}\text{and}\overrightarrow{B}=\hat{i}-2\hat{j}-3\hat{k}$, the angle which the $\overrightarrow{A}-\overrightarrow{B}$ vector makes with x-axis is

• A. ${\cos }^{-1}\left(\frac{1}{10}\right)$
• B. ${\cos }^{-1}\left(\frac{2}{\sqrt{10}}\right)$
• C. ${\cos }^{-1}\left(\frac{1}{\sqrt{10}}\right)$
• D. ${\cos }^{-1}\left(\frac{1}{5}\right)$

Answer 1

The correct option is C ${\cos }^{-1}\left(\frac{1}{\sqrt{10}}\right)$

$\overrightarrow{A}=4\hat{i}-2\hat{j}+6\hat{k}\text{and}\overrightarrow{B}=\hat{i}-2\hat{j}-3\hat{k}$
$\overrightarrow{A}-\overrightarrow{B}=3\hat{i}+9\hat{k}\text{x -axis}=\hat{i}$
$\cos \theta =\frac{(3\hat{i}+9\hat{k}).\left(\hat{i}\right)}{\sqrt{90}}\cos \theta =\frac{3}{\sqrt{90}}$
$\theta ={\cos }^{-1}\frac{1}{\sqrt{10}}$