Let a plane pass through points m (1.0-2) and m (1.2.2) and be parallel to vector a = (1.1.1)

Let a plane pass through points m (1.0-2) and m (1.2.2) and be parallel to vector a = (1.1.1)

Let the equation AX + by + CZ + D = 0 pass through two points, and substitute it into the plane equation: a-2c + D = 0A + 2B + 2C + D = 0. The normal vector of the equation is (a, B, c). Since the plane is parallel to vector a, its normal vector is perpendicular to vector a, that is, a * 1 + b * 1 + C * 1 = a + B + C = 0