Chapter 4: Lines and Planes
Consider two known points of a triangle and .
We can use these points to determine the slope and plug into the explicit equation:
Here we have replaced the unknown y-intercept with another constant, . We don’t really care what was so we’ll just move on with .
We know that is on the point, so let’s plug in an solve for .
Plug back in to our original equation with
A plane is defined by a point and a normal . The plane consists of all points for which is perpendicular to .
Or, using the dot product:
And to get a more commonly seen equation: