Find the rectangular equation for the surface given by by eliminating the paranmeter.
I'm having a bad day. I can see that . But, that's as far as I get. Any Help?
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