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Unformatted text preview: Equations of Planes In the first section of this chapter we saw a couple of equations of planes. However, none of those equations had three variables in them and were really extensions of graphs that we could look at in two dimensions. We would like a more general equation for planes. So, lets start by assuming that we know a point that is on the plane, . Lets also suppose that we have a vector that is orthogonal (perpendicular) to the plane, . This vector is called the normal vector . Now, assume that is any point in the plane. Finally, since we are going to be working with vectors initially well let and be the position vectors for P and P respectively. Here is a sketch of all these vectors. Notice that we added in the vector which will lie completely in the plane. Also notice that we put the normal vector on the plane, but there is actually no reason to expect this to be the case. We put it here to illustrate the point. It is completely possible that the normal vector does not touch the plane in any way.completely possible that the normal vector does not touch the plane in any way....
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- Fall '08