First slide

Direction ratios and direction cosines

Question

If $P = (0, 1, 2), Q = (4, - 2, 1), O = (0, 0, 0)$ then $∠ P O Q =$

Moderate

A

$\frac{π}{6}$
B

$\frac{π}{4}$
C

$\frac{π}{3}$
D

$\frac{π}{2}$

Solution

D.r’s of $\vec{O P}$ are $(0, 1, 2)$ ; D.r’s of $\vec{O Q}$ are $(4, - 2, 1)$
$\cos ∠ P O Q = \frac{0 - 2 + 2}{\sqrt{0 + 1 + 4} \sqrt{16 + 4 + 1}} = 0$
$\Rightarrow ∠ P O Q = \frac{π}{2}$

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