MATLAB: Orthagonal planes and normal vectors

plane

I have three planes:
3x +2y -z =18
3x – 8y -7z = -38
-22 + 18 -30 = -6
And I'd like to find normal vector to those planes, and then chech if these vectors are orthagonal to themselves, then check the if the planes are orthagonal. How can I do this thing? I'd be greateful for any help in this matter.

Best Answer

Hi M,
A plane satisfies the dot product equation equation
r dot v = const
where r is the position vector [x y z] and v = [vx vy vz] is a vector perpendicular to the plane. A vector perpendicular to the first plane is
v1 = [3 2 -1];
because dotting that into [x y z] produces the equation for the first plane. Similarly for the other two. A unit vector perpendicular to the plane is
n1 = v1/norm(v1) % normalized vector perpendicular to plane
and similarly for the other two. Then dot(n1,n2) tellls you if n1 and n2 are orthogonal, and similarly for the other possible pairs.
Planes are orthogonal if and only if their normal vectors are orthogonal.