Question

If the angle between the line x = (y - 1)/2 = (z - 3)/λ and the plane x + 2y + 3z = 4 is cos^-1(√(5/14)), then  λ equals

(A) 3/2

(B) 2/5

(C) 5/3

(D) 2/3

Answer 1

Answer is (D) 2/3

Direction ratios of the line are 1, 2 and l and direction ratios of normal to the plane are 1, 2 and 3. Therefore angle between line and plane is given by