MHT CET · Maths · Three Dimensional Geometry
If the direction cosines of a line are \(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\) then
- A \(2 < \mathrm{c} < 3\)
- B \(\mathrm{c}=\pm 3\)
- C \(\mathrm{c}=\pm \sqrt{3}\)
- D \(\mathrm{c}=\pm \frac{1}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{c}=\pm \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Given \(\ell=m=n=\frac{1}{c}\)
We know that \(\ell^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1 \Rightarrow \frac{3}{\mathrm{c}^{2}}=1 \Rightarrow \mathrm{c}^{2}=3 \Rightarrow \mathrm{c}=\pm \sqrt{3}\)
We know that \(\ell^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1 \Rightarrow \frac{3}{\mathrm{c}^{2}}=1 \Rightarrow \mathrm{c}^{2}=3 \Rightarrow \mathrm{c}=\pm \sqrt{3}\)
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