Question

The angle between the lines whose direction cosines are proportional to (1, 2, 1) and (2, –3, 6) is

• A. $\cos ^ { - 1 } \left( \frac { 2 } { 7 \sqrt { 6 } } \right)$
• B. $\cos ^ { - 1 } \left( \frac { 1 } { 7 \sqrt { 6 } } \right)$
• C. $\cos ^ { - 1 } \left( \frac { 3 } { 7 \sqrt { 6 } } \right)$
• D. $\cos ^ { - 1 } \left( \frac { 5 } { 7 \sqrt { 6 } } \right)$

Answer 1

Answer: (A)

$\cos ^ { - 1 } \left( \frac { 2 } { 7 \sqrt { 6 } } \right)$

Answer 2

$\theta = \cos ^ { - 1 } \left[ \frac { ( 1 ) ( 2 ) + ( 2 ) ( - 3 ) + ( 1 ) ( 6 ) } { \sqrt { 1 ^ { 2 } + 2 ^ { 2 } + 1 ^ { 2 } } \sqrt { 2 ^ { 2 } + ( - 3 ) ^ { 2 } + 6 ^ { 2 } } } \right]$

$\cos ^ { - 1 } \left[ \frac { 2 - 6 + 6 } { \sqrt { 6 } \sqrt { 49 } } \right] = \cos ^ { - 1 } \left[ \frac { 2 } { 7 \sqrt { 6 } } \right]$ .