Let ‘L’ be the line of intersection of the planes2x+3y+z=1  and x+3y+2z=2, if L makes an angle α with positive x-axis, then cosα equals.

The given planes are 2x+3y+z=1  and x+3y+2z=2The line of intersection of those two planes is along the vector n¯=ijk231132=i3-j3+k3Hence, the direction ratios of the line of intersection of two planes is ⟨1,−1,1⟩The angle made by the line with x- axis is α then cosα=±13