Here's the problem: "Let A = (-1,3,0), B = (3,2,4) and C = (1,-1,5).

a) Find the equation for the plane that passes through these three points."

My work:

I found AB and AC.

AB = 4i - j + 4k

AC = 2i - 4j + 5k

Then I took the cross product of the two vectors, AB x AC, and got 11i-12j-14k. So then I plugged in one of the sets of points into the equation and got 11(x-3) - 12(y-2) - 14(z-4), which lead me to 11x-12y-14z = -47.

Could someone check my work and tell me if I did this correctly? Thank you!