Equation of the line through the given points is 5−3x−3 = 1−4y−4 = 6−1z−1 ⇒ 2x− = −3y−4 = 5z−1 Any point on this line can be taken as (3 + 2λ, 4 – 3λ, 1 + 5λ) If this point lies on XY-plane then the z-coordinate is zero ⇒ 1 + 5 λ = 0 ⇒ λ = −51 Thus the required coordinates of the point are (3−52,4−3(−51),0) = (513,523,0)