Normal Vector

The vector Normal Vector Definition is a normal vector to the plane, that is to say, perpendicular to the plane.

Normal Vector

If P(x0, y0, z0) is a point on the plane, the vector Normal Vector Definition is perpendicular to vector vector normal, and its dot product is zero.

Normal Vector Equation

Therefore, the equation of the plane can be determined from a point and a normal vector.


Examples

1.Find the equation of the line r, that passes through the point (1, 0, 0) and is perpendicular to the plane x − y − z + 2 = 0.

Normal Vector Example     A = (1, 0, 0).

Normal Vector Solution


2.Find the equation of the plane, π, that passes through the point (1, 1, 1) and is perpendicular to the lines x = λ, y = 0, z = λ.

As the plane and the line are perpendicular, the direction vector of the line is a normal vector of the plane.

Linear Determination

Scalar Product

Scalar Product

Equation of the Plane Solution