As it turns out, is the equation of the plane.

The position vector, gives the coordinates of a point at

so the surface passes through the origin, (0, 0, 0).

Define vector, .

Define vector, .

Notice that any vector of the form may be written as a linear

combination of the constant vectors, and .

Therefore, the surface specified by is a plane.

Vectors, and lie in the plane, so their vector product (cross product) is perpendicular to the plane.

So, the equation of the plane is

which may be written as