Question

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

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (B)

4

Answer 2

Since $\alpha = \beta = \gamma \Rightarrow \cos ^ { 2 } \alpha + \cos ^ { 2 } \alpha + \cos ^ { 2 } \alpha = 1$

$\Rightarrow \alpha = \cos ^ { - 1 } \left( \pm \frac { 1 } { \sqrt { 3 } } \right)$

So, there are four lines whose direction cosines are

$\left( \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } \right) , \left( \frac { - 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } \right) , \left( \frac { 1 } { \sqrt { 3 } } , \frac { - 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } \right)$

$\left( \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { - 1 } { \sqrt { 3 } } \right)$.