Proving: All Points on Ax + By + Cz = 0 Lie in Plane Perpend. to Ai + Bj + Ck

[MozAngeles]

Homework Statement

The vector r = xi + yj + zk, called the position vector, points from the origin (0, 0, 0) to an arbitrary point in space with coordinates (x, y, z).

Use what you know about vectors to prove the following: All points (x, y, z) that satisfy the equation Ax + By + Cz = 0, where A, B and C are constants, lie in a plane that passes through the origin and that is perpendicular to the vector Ai + Bj + Ck.

Homework Equations

A∙B=0 ⇒A⊥B

The Attempt at a Solution

I have no idea how to begin this proof. I know that A∙B is necessary and sufficient condition for two vectors to be perpendicular to each other. I do not know what else i would put down...

 

[tiny-tim]

Hi MozAngeles!

The vector Ai + Bj + Ck ends at a point …

start by calling that point P, and calling a point on the plane Q.