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1. ⇒ (MHT CET 2021 21th September Evening Shift )

The co-ordinates of the point $P \equiv (1, 2, 3)$ and $O \equiv (0, 0, 0)$ , then the direction cosines of $\overset{―}{OP}$ are

A. $\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$

B. $\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$

C. $\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$

D. $\frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}}$

Correct answer option is (A)

We have $O \equiv (0, 0, 0)$ and $P \equiv (1, 2, 3)$

Hence direction ratios of $\overset{―}{OP}$ are

$\frac{1 - 0}{\sqrt{1^{2} + 2^{2} + 3^{2}}}, \frac{2 - 0}{\sqrt{1^{2} + 2^{2} + 3^{2}}}, \frac{3 - 0}{\sqrt{1^{2} + 2^{2} + 3^{2}}} = \frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$

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