Question

An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z – 1 = 0 and 5x + 8y + 2z + 14 = 0, is

(A) sin^-1(√(3/17))

(B) cos^-1(√(3/17))

(C) cos^-1(3/√17)

(D) sin^-1(3/√17)

Answer 1

Answer is (A) sin^-1(√(3/17))

Given:

3x + 4y + z – 1 = 0 and 5x + 8y +2z + 14 = 0

The direction of line of intersection of plans is given by

Direction ratios of line of intersection is (0, −1, 9)

Therefore, angle between plane x + y + z = 5 and line or intersection is θ.