3 Coincident Planes
- Kara Babcock
Three planes are coincident when they have the same or parallel normal vectors and their equations are scalar multiples of each other. In this example, the two planes are x - y + z = 3; 2x - 2y + 2z = 6; and 3x - 3y + 3z = 9. Notice from the example how they have parallel normal vectors, and how the coefficients of the second equation are all double the coefficients of the first equation, and the coefficients of the third equation are all three times the coefficients of the first equation.
How many points of intersection are there?