# Equation of lines and planes

1. Sep 25, 2006

### suspenc3

A few Questions:

a)when finding vector equations (for lines), what do you different when they give you a vector and a line parallel to this vector, and a vector and a line perpendicular to the vector.

b)concerning planes, can someone briefly explain the normal vector.

Thanks.

2. Sep 25, 2006

I'll try to help with b).

The easiest way to copletely determine a plane is with one point T1 = (x1, y1, z1) (belonging to the plane) and a vector n which is perpendicular to the plane, which we call the normal vector. Now, let T = (x, y, z) be any point in the plane. Obviously, n must be perpendicular to the vector $$\vec{T_{1}T}$$, which implies n(r-r1)=0 ...(1), where r1 is the radius vector determined by the point T1, and r the radius vector determined by the point T. Further on, (1) directly implies A(x-x1) + B(y-y1)+ C(z-z1) = 0, where n=Ai+Bj+Ck. This is a general equation of a plane.

3. Sep 25, 2006

### suspenc3

Yeah that explains it, so say they give you a point and a vector parallel to the plane, how would you get the Normal? Would you just cross the vector and the point?

4. Sep 25, 2006