Question

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ , $l ^ { 2 } + m ^ { 2 } - n ^ { 2 } = 0$ is given by

• A. $\frac { 2 \pi } { 3 }$
• B. $\frac { \pi } { 6 }$
• C. $\frac { 5 \pi } { 6 }$
• D. $\frac { \pi } { 3 }$

Answer 1

Answer: (D)

$\frac { \pi } { 3 }$

Answer 2

$l + m + n = 0 , l ^ { 2 } + m ^ { 2 } - n ^ { 2 } = 0$ and $l ^ { 2 } + m ^ { 2 } + n ^ { 2 } = 1$

Solving above equations, we get $m = \pm \frac { 1 } { \sqrt { 2 } } , n = \pm \frac { 1 } { \sqrt { 2 } }$and $l = 0$. $\therefore \theta = \frac { \pi } { 3 }$ or $\frac { \pi } { 2 }$.