question_answer

The angle between the lines \[3x=6y=2z\]and \[3x+2y+z-5=0=x+y-2z-3\] is

A) \[\frac{\pi }{6}\]            

B) \[\frac{\pi }{3}\]

C) \[\frac{\pi }{4}\]

D) \[\frac{\pi }{2}\]

Correct Answer: D

Solution :

[d]: The d.r? s of the first line are \[\frac{1}{3},\frac{1}{6},\frac{1}{2}\]...(i) The second line is along the vector The d.rs are - 5, 7, 1                     ?(ii) From (i) and (ii)\[\Rightarrow \]\[-\frac{5}{3}+\frac{7}{6}+\frac{1}{2}=0\]. \[\therefore \]The lines are perpendicular.