JEE MAIN - Mathematics (2024 - 29th January Evening Shift - No. 9)
Let $$\mathrm{P}(3,2,3), \mathrm{Q}(4,6,2)$$ and $$\mathrm{R}(7,3,2)$$ be the vertices of $$\triangle \mathrm{PQR}$$. Then, the angle $$\angle \mathrm{QPR}$$ is
$$\cos ^{-1}\left(\frac{7}{18}\right)$$
$$\frac{\pi}{6}$$
$$\cos ^{-1}\left(\frac{1}{18}\right)$$
$$\frac{\pi}{3}$$
Explanation
_29th_January_Evening_Shift_en_9_1.png)
Direction ratio of $$\mathrm{PR}=(4,1,-1)$$
Direction ratio of $$\mathrm{PQ}=(1,4,-1)$$
Now, $$\cos \theta=\left|\frac{4+4+1}{\sqrt{18} \cdot \sqrt{18}}\right|$$
$$\theta=\frac{\pi}{3}$$
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