pg. 717, #29 (moderate)

Find the equation of the plane passing through (1,0,-3), (0,-2,-4) and (4,1,6).

Solution:

Let v be the vector from (1,0,-3) to (0,-2,-4); v = <-1,-2,-1>. Let w be the vector from

(1,0,-3) to (4,1,6); w = <3,1,9>. Then desired normal is

Multiplying this normal by -1, the equation of the plane is

This reduces to 17x -6y -5z = 32. Check your work by verifying that (0,-2,-4) and (4,1,6) are on this

plane. They are: