Equation of a Plane with 2 Points and Perpendicular

[emma3001]

Homework Statement

Determine the equation of the plane that contains the points A(1, 2, 3) and B(2, 3, -1) and is perpendicular to the plane 3x + y + z + 1=0. I think I know how to do it with only one point, not two

The Attempt at a Solution

I know that v= normal so it would be (3, 1, 1). Then I could use point A and say (x-1, y-2, z-3)dot(3, 1, 1)=0
After expanding, I get 3x + y + z -8=0. Do I need to incorporate the other point?

 

[Vid]

No, you only need to use one point. Notice that if you had used the other point, you would have gotten the same equation.

 

[emma3001]

the answer in the book is 5x-13y-2z+27=0. Does it make sense that my answer is so different? Would they give the same answer?

 

[Vid]

Your normal vector is wrong. (3,1,1) is perpendicular to the given plane, but not the plane they want.