Question

The number of lines which are equally inclined to the axes is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is B 4

If a line makes angles $\alpha ,\beta ,\gamma$ with the axes we have $\alpha =\beta =\gamma$

$cos\alpha =cos\beta =cos\gamma$, or $l=m=n.$

$l^2+m^2+n^2=1$

$l^2+l^2+l^2=1$

$3l^2=1$
$l^2=\frac{1}{3}$

$\therefore l=\pm \frac{1}{\sqrt{3}}$

$\therefore (l,m,n)(-l,-m,-n)$ represent the d.c's of the same line.

Since there are four different groups of signs,

so there can be four different lines which makes equal angles with axes.