Plane Through a Given Point Perpendicular to a Given Line

Plane Through a Given Point Perpendicular to a Given Line

If a line has direction ratios:

$$a:b:c$$

then a plane perpendicular to the line has normal vector:

$$\vec n=a\hat i+b\hat j+c\hat k$$

Through $$P(x_1,y_1,z_1)$$, its equation is:

$$a(x-x_1)+b(y-y_1)+c(z-z_1)=0$$

Usage

- Used when a plane is required to be perpendicular to a given line.