Question

Write the formula for foot of perpendicular from point to plane.

Answer 1

By default, the equation of a plane is

ax + by + cz = d  

or  

ax +by + cz – d = 0  

Formula for foot of the perpendicular (p,q,r) from point (x1, y1, z1) is

$\frac{p - x_1}a=\frac{q - x_2}b=\frac{r - x_3}c = -\frac{ax_1 + by_1 + cz_1 -d}{a^2 + b^2 + c^2}$  

Image of the point ($x_1, y_1, z_1$) is given by

$\frac{p - x_1}a=\frac{q - y_2}b=\frac{r - z_3}c = -\frac{2(ax_1 + by_1 + cz_1 - d)}{a_2 + b_2 + c_2}$