Question

Find the equation of the perpendicular drawn from the point (1, –2, 3) to the plane 2x – 3y + 4z + 9 = 0. Also, find the coordinates of the foot of the perpendicular.

Answer 1

Let the foot of the perpendicular on the plane be A.

PA perpendicular to the plane

2x – 3y + 4z + 9 = 0

Dr’s of PA = 2, –3, 4

Equation of PA can be written as

\(\frac{x-1}{2}=\frac{y+2}{-3}=\frac{z-3}{4}=\lambda\)

General points of line PA = (2λ + 1, -3λ -2, 4λ + 3)

The point is on the plane hence

\(\therefore\) Coordinates of foot of perpendicular are (-1, 1, -1).