Finding A Particular Equation

"Describe and find an equation for the surface generated by all points (x,y,z) that are four units from the plane 4x - 3y + z = 10."

Firstly, I found a point P on the plane: P = (0,0,10). Then I constructed a vector whose initial point is (0,0,10) and terminal point is Q = (x,y,z):

The vector normal to the plane is

Does this appear to be the correct answer?

Re: Finding A Particular Equation

Quote:

Originally Posted by

**Bashyboy** "Describe and find an equation for the surface generated by all points (x,y,z) that are four units from the plane 4x - 3y + z = 10."

Firstly, I found a point P on the plane: P = (0,0,10). Then I constructed a vector whose initial point is (0,0,10) and terminal point is Q = (x,y,z):

The vector normal to the plane is

Does this appear to be the correct answer?

No it does not.** Almost**, but not correct. You just cannot drop the absolute values.

If then

Re: Finding A Particular Equation

Note that there are **two** planes that are a given distance from a given distance.