Determine the equation of the plane that passes through points (1,0,-1), (0,2,3), and (0,0,0).
Letting the equation of the plane be ax+by+cz+d=0
Skipping through the steps...
How do you know c=2?
You could use a normal vector to the plane and ANY point on the plane to get your equation.
Your plane goes through the origin. You have two vectors in the plane:
We use the fact that a crossing two vectors (cross-product) produces a vector that is normal to the plane spanned by these two vectors:
Now, since these vector is normal to the plane,