Question

Find the angle that the vector $\overrightarrow{A}=2\hat{i}+3\hat{j}-\hat{k}$ makes with y-axis.

• A. $\theta ={\cos }^{-1}\left(\frac{3}{\sqrt{14}}\right)$
• B. $\theta ={\cos }^{-1}\left(\frac{2}{\sqrt{14}}\right)$
• C. $\theta ={\cos }^{-1}\left(\frac{3}{\sqrt{16}}\right)$
• D. $\theta ={\cos }^{-1}\left(\frac{3}{\sqrt{28}}\right)$

Answer 1

The correct option is A $\theta ={\cos }^{-1}\left(\frac{3}{\sqrt{14}}\right)$

$\cos \theta =\frac{A_y}{A}=\frac{3}{\sqrt{{\left(2\right)}^2+{\left(3\right)}^2+{(-1)}^2}}=\frac{3}{\sqrt{14}}$

$\therefore \theta ={\cos }^{-1}\left(\frac{3}{\sqrt{14}}\right)$