Find the scalar equation of the plane through the points M(1,2,3) and N(3,2,-1) that is perpendicular to the plane with equation 3x + 2y + 6z +1 = 0.

1 answer

The normal to the given plane is [3,2,6]
Since the new plane is perpendicular to the old plane, [3,2,6] must be a direction vector in the new plane.
You can find vector MN, which would be a second direction vector in your new plane.
You now have a point M, and 2 direction vectors.
Find the equation of your new plane using your favourite method.
(let me know what you get)