Find an equation for the plane through the points (5,3,4),(−1,0,2),(0,2,−1).

Question

Find the equation.

The plane is: ______ ?

Answer 1

We need a normal vector for the plane the three given points define.

Let A(5,3,4)

B(-1,0,2) and

Γ(0,2,-1)

Then vector AB = < -6,-3,-2 > and BΓ = < 1,2 -3> and their cross product

AB x BΓ = <13,-20,-9>

Then the equation of the plane is 13x -20(y-2) -9(z+1) =0

13x -20y -9z = -31