Intercept and normal forms of a plane
Three-dimensional geometry and vector algebra · Mathematics
Study notes
Q: Write 2x + 3y + 6z = 12 in intercept and normal forms. Intercept: x/6 + y/4 + z/2 = 1. Normal: divide by √(4+9+36) = 7: (2/7)x + (3/7)y + (6/7)z = 12/7. So p = 12/7, direction cosines (2/7, 3/7, 6/7).