Now that we have a way of describing lines, we would like to develop a means of describing planes in three dimensions. We studied the coordinate planes and planes parallel to them in
Section 1.1. Each of those planes had one of the variables
or
equal to a constant. We can note that any vector in a plane with
constant is orthogonal to the vector
any vector in a plane with
constant is orthogonal to the vector
and any vector in a plane with
constant is orthogonal to the vector
This idea works in general to define a plane.
Just as two distinct points in space determine a line, three non-collinear points in space determine a plane. Consider three points
and
in space, not all lying on the same line as shown in
Figure 1.5.8.