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If $P=(0,1,2), Q=(4,-2,1), O=(0,0,0)$, then $\angle P O Q$ is equal to
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Verified Answer
The correct answer is:
$\frac{\pi}{2}$
We have,
Direction cosines of $O Q$ are
$4-0,-2-0,1-0$
i.e.
$4,-2,1$
Direction cosines of $O P$ are
$0-0,1-0,2-0$
i.e.
$0,1,2$
Then,
$\begin{aligned} \cos \theta & =l_1 l_2+m_1 m_2+n_1 n_2 \\ & =4 \cdot 0+(-2) \cdot 1+1 \cdot 2 \\ & =0-2+2=0 \\ \cos \theta & =0=\cos \frac{\pi}{2} \\ \theta & =\frac{\pi}{2}\end{aligned}$
Direction cosines of $O Q$ are
$4-0,-2-0,1-0$
i.e.
$4,-2,1$
Direction cosines of $O P$ are
$0-0,1-0,2-0$
i.e.
$0,1,2$
Then,
$\begin{aligned} \cos \theta & =l_1 l_2+m_1 m_2+n_1 n_2 \\ & =4 \cdot 0+(-2) \cdot 1+1 \cdot 2 \\ & =0-2+2=0 \\ \cos \theta & =0=\cos \frac{\pi}{2} \\ \theta & =\frac{\pi}{2}\end{aligned}$
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