Question

If direction ratios of two lines are $5 , - 12,13$ and $- 3,4,5$ then the angle between them is

• A. $\cos ^ { - 1 } ( 1 / 65 )$
• B. $\cos ^ { - 1 } ( 2 / 65 )$
• C. $\cos ^ { - 1 } ( 3 / 65 )$
• D. $\pi / 2$

Answer 1

Answer: (A)

$\cos ^ { - 1 } ( 1 / 65 )$

Answer 2

$\theta = \cos ^ { - 1 } \frac { ( - 15 - 48 + 65 ) } { \sqrt { 25 + 144 + 169 } \sqrt { 9 + 16 + 25 } }$

= $\cos ^ { - 1 } \left( \frac { 2 } { ( 13 \sqrt { 2 } ) ( 5 \sqrt { 2 } ) } \right)$ = $\cos ^ { - 1 } \left( \frac { 1 } { 65 } \right)$.