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

Answer: (B)

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