The direction cosines of the line passing through $P(2,3-1)$ and the origin are

The direction cosines of the line passing through $P(2,3-1)$ and the origin are
  1. $\frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{1}{\sqrt{14}}$
  2. $\frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}$
  3. $\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}$
  4. $\frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{-1}{\sqrt{14}}$

Solution

The direction cosines of $O P$ $\begin{aligned} & =\left(\frac{-2}{\sqrt{4+9+1}}, \frac{-3}{\sqrt{4+9+1}}, \frac{1}{\sqrt{4+9+1}}\right) \\ & =\left(\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\right) \end{aligned}$

Asked in: AP EAMCET 2005

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