How Do You Find The Cartesian Equation Of A Plane?
The Cartesian equation of a plane in space is often very helpful when attempting to find its characteristics. • Find a normal vector. Sometimes this will be given, but often you will have to figure it out from other givens. For the purposes of this article, the normal vector is defined as n = < A, B, C> where n is a vector, and A, B, and C are scalars. • Find a point on the line. Usually this is a given, although occasionally you will have to come up with one based on the equation of a line. If you are given parametric equations, the easiest way to do this is to find the point where t = 0. For the purposes of this article, the point is defined as P(x1, y1, z1) • Plug these values into the equation for a plane. A(x-x1)+B(y-y1)+C(z-z1)=0 Simplify the equation. This will yield: Ax-Ax1+By-By1+Cz-Cz1=0. Remembering that x1, y1, and z1 are scalars, you can add them together and then add the opposite of that number to the other side of the equation. This value is known as D.
