question_answer

Let L be the line of intersection of the planes \[2x+3y+z=1\]and \[x+3y+2z=2\]. If L makes an angle\[\alpha \]with the positive x-axis, then \[\cos \alpha \] equals

A) 1         

B) \[\frac{1}{\sqrt{2}}\]

C) \[\frac{1}{\sqrt{3}}\]                 

D) \[\frac{1}{2}\]

Correct Answer: C

Solution :

[c]: Direction cosines of the line, Then, \[\cos \alpha =\frac{3}{\sqrt{9+9+9}}=\frac{1}{\sqrt{3}}.\]