Position, Direction, and Normal Vectors

A position vector of a plane p is a vector P such that P is a point on the plane. A direction vector of p is a vector D from one point of p to another. A normal vector of p is a vector N which is perpendicular to every direction vector of p. These vectors are illustrated in Figure 10.5.5.

Figure 10.5.5: Position, Direction, and Normal Vectors

We shall often find it convenient to write a scalar equation

ax + by + cz = d

for a plane in vector form,

(ai + bj + ck) · X = d.

We call this a vector equation for the plane.