Question

The number of straight lines that are equally inclined to the three-dimensional coordinate axes, is

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

Since, $\alpha =\beta =\gamma \Rightarrow {\cos }^2\alpha +{\cos }^2\alpha +{\cos }^2\alpha =1$
$\Rightarrow \alpha +{\cos }^{-1}(\pm \frac{1}{\sqrt{3}})$
So, there are four line whose $D{C}^{\prime }s$ are
$(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}),(\frac{-1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}),(\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}},\frac{1}{\sqrt{3}})(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}})$.