CUET · MATHS · PYQ PAPER 2025
The direction cosines of a line equally inclined with the co-ordinate axes are :
- A (1, 1, 1)
- B \(\left(\frac{1}{3}, \frac{1}{3}, \frac{1}{3}\right)\)
- C \(\left( \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\right)\)
- D \(\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(C) \(\left( \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\right)\)
Step-by-step Solution
Detailed explanation
\(l=m=n=\cos\alpha\) \(l^2+m^2+n^2=1\) \(3\cos^2\alpha=1\) \(\cos\alpha=\pm\frac{1}{\sqrt{3}}\) Direction cosines are \(\left( \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\right)\)
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