The intersection of the planes 2x−y−3z=8 and x+2y−4z=14 is the line L. The value of 'a' for which  the line L is perpendicular to the line through (a,2,2) and (6,11,−1) is

Vector along the line of intersection of planes isi^j^k^2−1−312−4=10i^+5j^+5k^This vector is perpendicular to the segment joining the points (a, 2, 2) and (6, 11, -1). ∴ 10(a−6)+5(2−11)+5(2+1)=0⇒ a=9