The co-ordinates of the $\mathrm{P} \equiv(1,2,3)$ and $\mathrm{O} \equiv(0,0,0)$, then the direction…

The co-ordinates of the $\mathrm{P} \equiv(1,2,3)$ and $\mathrm{O} \equiv(0,0,0)$, then the direction cosines of $\overline{\mathrm{OP}}$ are
  1. $\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$
  2. $\frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}$
  3. $\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}$
  4. $\frac{2}{\sqrt{29}}, \frac{3}{\sqrt{29}}, \frac{4}{\sqrt{29}}$

Solution

We have $\mathrm{O} \equiv(0,0,0)$ and $\mathrm{P} \equiv(1,2,3)$ Hence direction ratio $\overline{\mathrm{OP}}$ are $\frac{1-0}{\sqrt{1^2+2^2+3^2}}, \frac{2-0}{\sqrt{1^2+2^2+3^2}}, \frac{3-0}{\sqrt{1^2+2^2+3^2}}=\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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