Question

If the direction ratios of two lines are given by and $l + 2 m + 3 n = 0$, then the angle between the lines is

• A. $\pi / 2$
• B. $\pi / 3$
• C. $\pi / 4$
• D. $\pi / 6$

Answer 1

Answer: (A)

$\pi / 2$

Answer 2

By solving two equations,

$\left( l _ { 1 } , m _ { 1 } , n _ { 1 } \right) = ( 2 \sqrt { 2 } - 3 , - \sqrt { 2 } , 1 )$

$\left( l _ { 2 } , m _ { 2 } , n _ { 2 } \right) = ( - 2 \sqrt { 2 } - 3 , \sqrt { 2 } , 1 )$

$l _ { 1 } l _ { 2 } + m _ { 1 } m _ { 2 } + n _ { 1 } n _ { 2 } = 0$

∴ The angle between them is $\pi / 2$ .