Question

If vector $\vec{r}$ with d.c.s. $l,m,n$ is equally inclined to the co-ordinate axes, then the total number of such vectors is

• A. 4
• B. 6
• C. 8
• D. 2

Answer 1

Answer: (C)

$\overline{r}=|\overline{r}|\left(\pm \frac{1}{\sqrt{3}}\hat{i}\pm \frac{1}{\sqrt{3}}\hat{j}\pm \frac{1}{\sqrt{3}}\hat{k}\right)$
For equally inclined to co-ordinate axes.
$\alpha =\beta =\gamma$ and
$1=m=n$
Since, $1^2+m^2+n^2=1$
$\Rightarrow 31^2=1$
$\Rightarrow 1^2=\frac{1}{3}$
$\therefore l=\pm \frac{1}{\sqrt{3}}=m=n$
$\Rightarrow 1,m,n$ each has $2$ choices.
$\therefore$ total lines $=2^3$