Question

The angle between the lines whose direction cosines are connected by the relations $l + m + n = 0$and $2 l m + 2 n l - m n = 0$, is

• A. $\frac { \pi } { 3 }$
• B. $\frac { 2 \pi } { 3 }$
• C. $\pi$
• D. None of these

Answer 1

Answer: (B)

$\frac { 2 \pi } { 3 }$

Answer 2

Eliminating n, we have $( 2 l + m ) ( l - m ) = 0$

When $2 l + m = 0$ then $\frac { l } { 1 } = \frac { m } { - 2 } = \frac { n } { 1 }$

When $l - m = 0$ then $\frac { l } { 1 } = \frac { m } { 1 } = \frac { n } { - 2 }$

$\therefore$ Direction ratios are 1, – 2, 1 and 1, 1, – 2.

$\cos \theta = \frac { \sum a _ { 1 } a _ { 2 } } { \sqrt { \left( \sum a _ { 1 } ^ { 2 } \right) } \cdot \sqrt { \left( \sum a _ { 2 } ^ { 2 } \right) } } = - \frac { 1 } { 2 }$