# Drawing a plane

• Dec 25th 2011, 03:00 PM
dwsmith
Drawing a plane
How can I draw a plane with 2 vectors coming out of it from one point at 2 different angles?

It is a plane of the form ax + by + cz = 0 with 2 vectors <a,b,c> and <u,v,w> coming out of the plane from the same point.
• Dec 25th 2011, 03:19 PM
Plato
Re: Drawing a plane
Quote:

Originally Posted by dwsmith
How can I draw a plane with 2 vectors coming out of it from one point at 2 different angles?
It is a plane of the form ax + by + cz = 0 with 2 vectors <a,b,c> and <u,v,w> coming out of the plane from the same point.

Actually that question really is confused.
For one, there is only one angle between any two vectors.

A plane $\displaystyle ax+by+cz=0$ contains the origin $\displaystyle (0,0,0)$.
But more important, the vector $\displaystyle <a,b,c>$ is perpendicular to any vector parallel to that plane.

Now maybe you can rephrase the question.
• Dec 25th 2011, 03:22 PM
dwsmith
Re: Drawing a plane
Quote:

Originally Posted by Plato
Actually that question really is confused.
For one, there is only one angle between any two vectors.

A plane $\displaystyle ax+by+cz=0$ contains the origin $\displaystyle (0,0,0)$.
But more important, the vector $\displaystyle <a,b,c>$ is perpendicular to any vector parallel to that plane.

Now maybe you can rephrase the question.

By 2 different angles, I meant that <a,b,c> comes out at a 90 degree angle and the other one comes from the same point at some other angle.
• Dec 25th 2011, 03:37 PM
Plato
Re: Drawing a plane
Quote:

Originally Posted by dwsmith
By 2 different angles, I meant that <a,b,c> comes out at a 90 degree angle and the other one comes from the same point at some other angle.

Well that is somewhat clearer.
So to the OP.
Any two non-parallel vectors and a point determine a unique plane.
Given vectors $\displaystyle U~\&~V$ and point $\displaystyle (l,m,n)$
the plane they determine is $\displaystyle (U\times V)\cdot<x-l,y-m,z-n>=0$
• Dec 25th 2011, 03:38 PM
dwsmith
Re: Drawing a plane
Quote:

Originally Posted by Plato
Well that is somewhat clearer.
So to the OP.
Any two non-parallel vectors and a point determine a unique plane.
Given vectors $\displaystyle U~\&~V$ and point $\displaystyle (l,m,n)$
the plane they determine is $\displaystyle (U\times V)\cdot<x-l,y-m,z-n>=0$

I am trying to draw this with the tikz latex package.
• Dec 30th 2011, 03:21 PM
HallsofIvy
Re: Drawing a plane
As far as I know, LaTeX is a text formating language (with some diagram capabilities), not a "graphics" program. There is no way of "drawing" in LaTeX except by inserting graphics created through another program.