12.5: Equations of Lines and Planes

Question

Find an equation of the plane.
The plane through the point (7, −8, −4) and parallel to the plane 9x − y − z = 1

Answer 1

Let n = The normal vector for the plane = <9, -1, -1>

 

The general equation of a plane is:

 

n * <x-x0, y-y0, z-z0> = 0

<9, -1, -1> * <x-7, y+8, z+4> = 0

9(x-7) -1(y+8) -1(z+4) = 0

9x - 63 - y - 8 - z - 4 = 0

9x - y - z = 63 + 8 + 4

 

9x - y - z = 75