The vector is a normal vector to the plane, that is to say, perpendicular to the plane.
If P(x0, y0, z0) is a point on the plane, the vector is perpendicular to vector , and its dot product is zero.
Therefore, the equation of the plane can be determined from a point and a normal vector.
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.
A = (1, 0, 0).
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.