From Vector to Plane
From Vector to Plane
Any nonzero vector defines a unique plane in 3D. Except for planes through the origin, every plane is defined by a unique vector. This vector is normal (perpendicular) to the plane. In the equation of the plane , with as the defining vector, , which is the square of the norm (length) of the vector.
Ax+By+Cz=D
(A,B,C)
D=++
2
A
2
B
2
C
A vector norm is a length. A normal vector is perpendicular to a plane or line.