AP EAMCET · Maths · Three Dimensional Geometry
The direction cosines of the line passing through \(P(2,3-1)\) and the origin are
- A \(\frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
- B \(\frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
- C \(\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
- D \(\frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{-1}{\sqrt{14}}\)
Answer & Solution
Correct Answer
(C) \(\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
Step-by-step Solution
Detailed explanation
The direction cosines of \(O P\) \(\begin{aligned} & =\left(\frac{-2}{\sqrt{4+9+1}}, \frac{-3}{\sqrt{4+9+1}}, \frac{1}{\sqrt{4+9+1}}\right) \\ & =\left(\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\right) \end{aligned}\)
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