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Question
If P(0, 1, 2), Q(4, –2, 1) and O(0, 0, 0) are three points, then ∠POQ =
Options
\[\frac{\pi}{6}\]
\[\frac{\pi}{4}\]
\[\frac{\pi}{3}\]
\[\frac{\pi}{2}\]
Solution
\[\frac{\pi}{2}\]
\[O P^2 = \left( 0 - 0 \right)^2 + \left( 1 - 0 \right)^2 + \left( 2 - 0 \right)^2 = 0 + 1 + 4 = 5\]
\[Q O^2 = \left( 0 - 4 \right)^2 + \left( 0 + 2 \right)^2 + \left( 0 - 1 \right)^2 = 16 + 1 + 4 = 21\]
\[Since, P Q^2 = O P^2 + Q O^2 \]
\[Hence, ∠POQ = \frac{\pi}{2}\]
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