Review Presentation: Equation of a Plane

In order to find the equation of a plane, you must use the formula:
a(x-x1) + b(y-y1) + c(z-z1) + 0
When asked to find the equation of a plane, you will be given three points.  The first step is to choose one point to be your initial, one point to be u, and one point to v.  But, since they are points, you must make them into vectors by using your initial point and doing: terminal - initial.
(1,2,3)v
(-1,5,4)u
(o,-3,7)i
u = <-1,8,-3>
v = <1,5,-4>

Now you must place your vectors into a cross product (u x v) so that you can find your a,b, and c.
     i     j     k     i     j
    -1   8    -3   -1    8
     1   5    -4    1    5
u x v = <-17,-7,-3>
Now you plug these into your original equation, with x1, y1, and z1, being your points from your initial.

Final answer = -17x - 7y -3z = 0