SOLUTION: Please solve the following for me. Find the equation of the plane through the three points (1,-1,-1),(-3,2,-1) and (-2,3,0)

Find two non-parallel vectors both parallel to or "in" the plane and 
take their cross product to find a normal vector n to the plane.




Then the equation of the plane will be this dot product set equal to 0
so that the normal be perpendictular to the plane.

 n•

or

 

which is known as the "point-normal" form of the equation of a plane:

---------------------------------

To find two nonparallel vectors both parallel to or "in" the plane, we subtract
coordinates of any two pairs of the points to find two such vectors: 





Now we cross those two vectors to get a vector which is perpendicular to
both those vectors, and therefore perpendicular (normal) to the plane.



n = 

So substituting in the point-normal equation of a plane:











Edwin