Question

Let the direction - cosines of the line which is equally inclined to the axis be $\pm \frac{1}{\sqrt{k}}$. Find $k$ ?

• A. $2$
• B. $3$
• C. $5$
• D. $6$

Answer 1

The correct option is B $3$

We know sum of the squares of the direction cosines is one.

But it is given that $\alpha =\beta =\gamma$

$\therefore co{s}^2\alpha +co{s}^{\alpha }+co{s}^2\alpha =1$

$3co{s}^2\alpha =1$

$co{s}^2\alpha =\frac{1}{3}$

Thus $\cos \alpha =\frac{1}{\sqrt{3}}$

$\therefore \frac{1}{\sqrt{k}}=\frac{1}{\sqrt{3}}$

Taking squares on both sides we get

$\therefore k=3$