A person standing at $O(0,0,0)$ is watching an aeroplane which is at the coordinate point $A(4,0,3)$. At the same time he saw a bird at the coordinate point $B(0,0,1)$. Find the angles which $\overrightarrow{BA}$ makes with the $x$, $y$ and $z$ axes.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\cos^{-1}\left(\frac{2}{\sqrt{5}}\right), 90^\circ, \cos^{-1}\left(\frac{1}{\sqrt{5}}\right)$ ##
$\overrightarrow{BA} = \overrightarrow{OA} - \overrightarrow{OB} = (4\hat{i} + 3\hat{k}) - \hat{k} = 4\hat{i} + 2\hat{k}$
$\overrightarrow{BA} = \frac{4}{\sqrt{20}}\hat{i} + \frac{2}{\sqrt{20}}\hat{k} = \frac{2}{\sqrt{5}}\hat{i} + \frac{1}{\sqrt{5}}\hat{k}$
So, the angles made by the vector $\overrightarrow{BA}$ with the $x$, $y$ and $z$ axes are respectively:
$\cos^{-1}\left(\frac{2}{\sqrt{5}}\right),\ \frac{\pi}{2},\ \cos^{-1}\left(\frac{1}{\sqrt{5}}\right)$