Question

The length of the projection of the line segment joining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + z = 7 is

(A) 2/3

(B) 1/3

(C) √(2/3)

(D) 2/√3

Answer 1

Answer is (C) √(2/3)

We have the points A(5, −1, 4) and B(4, −1, 3) which join a line segment. Now,

AB = √((4 - 5)² + (-1 - (-1))² + (3 - 4)²) = (1 + 1)  = 2

The direction ratio of AB is <1, 0, 1>.

Let the angle between line AB and the plane be θ.

sinθ = 2/√6

cosθ = 1/√3

The projection of line AB on the plane is

ABcosθ = √(2/3)