JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(P(3,2,3), Q(4,6,2)\) and \(R(7,3,2)\) be the vertices of \(\triangle \mathrm{PQR}\). Then, the angle \(\angle \mathrm{QPR}\) is
- A \(\frac{\pi}{6}\)
- B \(\cos ^{-1}\left(\frac{7}{18}\right)\)
- C \(\cos ^{-1}\left(\frac{1}{18}\right)\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
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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