Planes in Space

To determine a plane we need a point and two linearly independent vectors (its direction vectors):

In coordinates:

If we have:

where n is a normal vector, that is, a vector orthogonal to every vector in the direction of π.

Then

NOTE:

Example:

Exercises:

1.- Find the plane that is perpendicular to the straight line r and passes through the point (-2,1,2), where:

2.- Find the plane that contains the origin and the straight line s:

Solutions:

1) 2x - z + 6 = 0: 2) 2x + 9y - 3z = 0