Question

If D.C's of two liens satisfy the relations $3 l + m + 5 n = 0$ and $6 m n - 2 n l + 5 l m = 0$, the angle between them is

• A. $\operatorname { Cos } ^ { - 1 } \left( \frac { 1 } { 6 } \right)$
• B. $\operatorname { Cos } ^ { - 1 } \left( \frac { 1 } { 3 } \right)$
• C. $\frac { \pi } { 2 }$
• D. $\operatorname { Cos } ^ { - 1 } \left( \frac { 3 } { 4 } \right)$

Answer 1

Answer: (A)

$\operatorname { Cos } ^ { - 1 } \left( \frac { 1 } { 6 } \right)$

Answer 2

Eliminating m from the given relations

we get $l ^ { 2 } + 3 \ln + 2 n ^ { 2 } = 0$

i.e.$( l + 2 n ) ( l + n ) = 0$ ;

i.e. $\frac { l } { - 2 } = \frac { n } { 1 }$or

Hence using 1st leation $\frac { l } { - 2 } = \frac { m } { 1 } = \frac { n } { 1 }$or $\frac { l } { - 1 } = \frac { m } { - 2 } = \frac { n } { 1 }$ hold. The angle between these lines is given by

$\cos \theta = \frac { 2 - 2 + 1 } { \sqrt { 4 + 1 + 1 } \sqrt { 1 + 4 + 1 } } = \frac { 1 } { 6 }$