Question

Find the distance of the point (4, 1, 1) from the lines x + y + z – 4 = 0 = x – 2y – 2z – 4.

Answer 1

Let a, b, c be the direction ratios of the line. Since, the line is perpendicular to the normal to the plane, so

a + b + c = 0

and a – 2b – 2c = 0

Solving, we get

Let the point of intersection of the line with z = 0 plane.

Putting z = 0 in the given equations we get

x + y = 4, x – 2y = 4

Solving, we get x = 4, y = 0

Hence, the equation of the line is