Find an orthogonal vector to 2 vector I have the following problem:
A B C D are the 4 consecutive summit of a parallelogram, and have the following coordinates
A(1,-1,1);B(3,0,2);C(2,3,4);D(0,2,3)
I must find a vector that is orthogonal to both CB and CD. 
How? Is there some kind of formula?
Thanks,

There are lots of ways to do this. Here are a few:


*

*Calculate the cross product of CB and CD. This is automatically perpendicular to both. (If you don't know what the cross product is, this may seem a little like a magic formula, and you should check that it's true if you use it.)

*Find a vector equation of the plane passing through B, C and D, and use it to find a Cartesian equation of the same plane. Read off a normal vector. This is perpendicular to everything in the plane, and CB and CD are in the plane.

*Find CB, and read off two linearly independent vectors u and v perpendicular to CB; these span a plane of "directions perpendicular to CB". Some vector au + bv should then be perpendicular to CD. (In fact, lots probably will. Try choosing a=1 or b=1 to simplify your life a little.)

