11.4 Lines and Planes In Space

In this lesson, we learned how to find the parametric and symmetric equations of a line in a 3-D space and how to find the angle and distance between two planes. In this blog, I'm going to focus on planes. The basic equation is:

a(x-x1) + b(y-y1) + b(z-z1) = 0

In this equation:

• a,b,c are the x, y, and z components of a perpendicular (normal) vector. n = <a,b,c>
• x1, y1, and z1 are the coordinates of a point on the plane.
• x,y, and z are variables. 

Many problems will give hints and ask you to find the equation of a plane. In the following example, a point on the plane and a perpendicular vector are given: