Question

If the direction cosines of a line are $ \left( \frac{1}{c},\frac{1}{c},\frac{1}{c} \right), $ then

• A. $ 0 < c < 1 $
• B. $ c>2 $
• C. $ c=\pm \sqrt{2} $
• D. $ c=\pm \sqrt{3} $
• E. $ c=\pm 3 $

Answer 1

Answer: (D)

Since, DCs of a line are $ \left( \frac{1}{c},\frac{1}{c},\frac{1}{c} \right) $ .
$ \therefore $ $ {{\left( \frac{1}{c} \right)}^{2}}+{{\left( \frac{1}{c} \right)}^{2}}+{{\left( \frac{1}{c} \right)}^{2}}=1 $
$ \Rightarrow $ $ {{c}^{2}}=3\Rightarrow c=\pm \sqrt{3} $