Question

If a vector A is given as $A=4\hat{i}+3\hat{j}+12\hat{k}$, then the angle subtended with the x-axis is :

• A. ${\sin }^{-1}\left[\begin{array}{c}\frac{4}{13}\end{array}\right]$
• B. ${\sin }^{-1}\left[\begin{array}{c}\frac{3}{13}\end{array}\right]$
• C. ${\cos }^{-1}\left[\begin{array}{c}\frac{3}{13}\end{array}\right]$
• D. ${\cos }^{-1}\left[\begin{array}{c}\frac{4}{13}\end{array}\right]$

Answer 1

The correct option is D ${\cos }^{-1}\left[\begin{array}{c}\frac{4}{13}\end{array}\right]$

Let $\alpha$ is the angle which A makes with x-axis, then

$\cos \alpha =\frac{A_x}{A}=\frac{4}{\sqrt{4^2+3^2+{12}^2}}=\frac{4}{13}$

$\alpha ={\cos }^{-1}\left[\begin{array}{c}\frac{4}{13}\end{array}\right]$