Parametric Equations of a Plane

[lostinphys]

Here is my question: When given three distict points A, B, C, find the parametric equations for the plane through these three points.
I was able to get the plane through these three points, first of all by getting the normal vector n = ABxAC, then by multiplying this vector by [(X-Xo)+(Y-Yo)+(Z-Zo)]. Where Xo, Yo, and Zo are the coordinates of point A.
But from this point on I don't know how to obtain the parametric equations from the plane equation. Please help!

 

[JG89]

Here is my question: When given three distict points A, B, C, find the parametric equations for the plane through these three points.
I was able to get the plane through these three points, first of all by getting the normal vector n = ABxAC, then by multiplying this vector by [(X-Xo)+(Y-Yo)+(Z-Zo)]. Where Xo, Yo, and Zo are the coordinates of point A.
But from this point on I don't know how to obtain the parametric equations from the plane equation. Please help!

You can first find the vector equation then convert it to parametric equations.

You have the three points A, B, and C. Find vector AB and vector AC then double check to make sure that they are not collinear (as you need two non-collinear direction vectors for equation of a plane). You now have two direction vectors and pick any point A, B, or C and you should have the vector equation. From there you can find the parametric equations.