Three Dimensional Geometry Question 14
Question 14 - 2024 (29 Jan Shift 2)
Let $P(3,2,3), Q(4,6,2)$ and $R(7,3,2)$ be the vertices of $\triangle PQR$. Then, the angle $\angle QPR$ is
(1) $\frac{\pi}{6}$
(2) $\cos ^{-1}\left(\frac{7}{18}\right)$
(3) $\cos ^{-1}\left(\frac{1}{18}\right)$
(4) $\frac{\pi}{3}$
Show Answer
Answer (4)
Solution
Direction ratio of $PR=(4,1,-1)$
Direction ratio of $PQ=(1,4,-1)$
Now, $\cos \theta=\left|\frac{4+4+1}{\sqrt{18} \cdot \sqrt{18}}\right|$
$\theta=\frac{\pi}{3}$
