Question

2. The general equation of a plane is Ax + By + Cz = D, where A, B, C, and D are real numbers and A is nonnegative. Find the equation of the plane containing the points (3, 0, 0), (0, 8, 0), and (0, 0, 6). Show each step of your process. Then graph the plane.

(I'm sooooo lost!)

Answer 1

Let say the points are
R(3,0,0)
S(0,8,0)
T(0,0,6)
The plane contains those points and \(\vec {RS}=<-3, 8, 0>\) , \(\vec {RT}=<-3, 0, 6>\)
The normal vector of the plane is defined by \(\vec {RS}\) x \(\vec {RT}\) =<48,18,24>
From those, we have the equation of the plane is 48x +18y +24z =D
you just plug either of the points into the equation above to solve for D, re-plug the result into the equation to get the answer
For graphing, it's not hard, I think you can handle. :)