Question

The angle between $\overrightarrow{R}=2\hat{i}+3\hat{j}-4\hat{k}$ and y-axis is

• A. ${\cos }^{-1}\left(\frac{2}{\sqrt{29}}\right)$
• B. ${\cos }^{-1}\left(\frac{3}{\sqrt{29}}\right)$
• C. ${\sin }^{-1}\left(\frac{3}{\sqrt{29}}\right)$
• D. ${\tan }^{-1}\left(\frac{3}{\sqrt{29}}\right)$

Answer 1

Answer: (B)

${\cos }^{-1}\left(\frac{3}{\sqrt{29}}\right)$

$\hat{j}$ is the unit vector along y-axis
Required angle $\theta ={\cos }^{-1}\frac{(2\hat{i}+3\hat{j}-4\hat{k})\cdot \hat{j}}{\sqrt{29}\sqrt{1}}={\cos }^{-1}\frac{3}{\sqrt{29}}$