Question

If $P=(0,1,2),Q=(4,-2,1)$ and $O=(0,0,0)$, then $\angle POQ$

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D $\frac{\pi }{2}$

The three points are as given.
The position vector of point P i.e. $vector$ $OP$ is given by $(0,1,2)$
The position vector of point Q i.e. $vector$ $OQ$ is given by $(4,-2,1)$
So, the angle $POQ$ will be obtained by the dot product of $OP$ and $OQ$.
$\cos \theta =\frac{OP.OQ}{|OP|\times |OQ|}$
$\cos \theta =0$
$\therefore \theta$ = ${90}^o$