Login/Sign Up
Home » If vector with d.c.s. is equally inclined to the co-ordinate axes, then the total number of such vectors is (A) 4 (B) 6 (C) 8 (D) 2
If vector \bar{r} with d.c.s. 1, \mathrm{~m}, \mathrm{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
maths | Maths
If vector \bar{r} with d.c.s. 1, \mathrm{~m}, \mathrm{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

Correct option is

(C) 8

\overline{\mathrm{r}}=|\overline{\mathrm{r}}|\left(\pm \frac{1}{\sqrt{3}} \hat{\mathrm{i}} \pm \frac{1}{\sqrt{3}} \hat{\mathrm{j}} \pm \frac{1}{\sqrt{3}} \hat{\mathrm{k}}\right)

For equally inclined to co-ordinate axes.

\alpha=\beta=\gamma and 1=\mathrm{m}=\mathrm{n}

Since, 1^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1

\begin{array}{l} \Longrightarrow 3 \mathrm{l}^{2}=1 \\ \Longrightarrow \mathrm{l}^{2}=\frac{1}{3} \end{array}

\therefore 1=\pm \frac{1}{\sqrt{3}}=\mathrm{m}=\mathrm{n} \Rightarrow 1, \mathrm{~m}, n each has

2 choices.

\therefore total lines =2^{3}

i

More Material