3D Geometry

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line, x/1 = y/4 = z/5 is Q, then PQ is equal to:

  1. 3√5
  2. 2√42
  3. √42
  4. 6√5

Solution

(x - 1)/1 = (y + 2)/4 = (z - 3)/5 = λ

Let midpoint of PQ be M which lines on the plane

M(x, y, z) = (1 + λ, 4λ - 2, 5λ + 3)

2(1 + λ) + 3(4λ - 2) - 4(5λ + 3) + 22 = 0

- 6λ + 6 = 0

λ = 1

M (2, 2, 8), P (1, -2, 3)

PM = √42

PQ = 2√42

The correct option is B.