Describe each plane, 8x-5y=-40z

Apologies for this being a kind of stupid question...

Homework Statement

Describe each plane

(a) $$8x-5y=-40z$$

Homework Equations

Probably have to find the x, y, and z intercepts.

The Attempt at a Solution

I would assume that in order to find the x intercept you set y and z equal to zero. And the same idea for the other two.

THe answer that I got was (0, 0, 0). Am I doing this wrong?

tiny-tim
Homework Helper
$$8x-5y=-40z$$I would assume that in order to find the x intercept you set y and z equal to zero. And the same idea for the other two.

THe answer that I got was (0, 0, 0). Am I doing this wrong?

Hi paralian!

No, you're completely correct …

the plane intersects all three axes at the origin, (0, 0, 0).

erm … wasn't that obvious?

HallsofIvy
Homework Helper
Since there are an infinite number of planes that contain (0,0,0), you might want to give some other points also to "describe" the plane. Three points determine a plane.

Defennder
Homework Helper
What is required to answer such a question?

tiny-tim
Homework Helper
Hi Defennder!

Hint: Forget about axes … what defines a particular plane through a given point?

Defennder
Homework Helper
The dot product of the normal vector to the plane and a vector lying on the plane through that point?

tiny-tim
Homework Helper
The dot product of the normal vector to the plane and a vector lying on the plane through that point?

Well, that will always be zero …

but what defines the plane?

(what makes one plane different from another plane?)

HallsofIvy