Let L be the line of intersection of the planes  2x+3y+z=1and x+3y+2z=2. If L makes an angle  α with the positive x-axis then cosα is

The line of intersection of two planes is perpendicular to the both normal vectors. The normal vectors to the given planes are  n1¯=2i+3j+k,and  n2¯=i+3j+2k,The vector along line of intersection of two planes is  n1¯×n2¯=ijk231132=i3−j3+k3Hence the direction cosines of line  are of intersection of two plane is  39+9+9,−39+9+9,39+9+9=13,−13,13Therefore,  cosα=13