Vectors & Planes: Proving Perpendicularity to Plane Passing through Origin

[madah12]

Homework Statement

The vector -; = Xl + yj + zk, called the position vector,
points from the origin (0. 0, o) 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 Care constants,lie in a plane
that passes through the origin and that is perpendicular to the vector
Ai + Bj + ck. Sketch this vector and the plane.

Homework Equations

if A . B = 0 then A is perpendicular to B

The Attempt at a Solution

I think I first should find an equation for a vector that lies in this plane then if the cross product is zero then it is perpendicular but I don't know anything about linear algebra or 3 dimensional space and this is from a physics text.

 

[madah12]

any hints? and what are the things that I should know as a prerequisite to solve such problem because I didn't study anything like it before.