# Cross Product

1. ### quantumfoam

127
What is the cross product of a constant and a vector? I know that the cross product between two vectors is the area of the parallelogram those two vectors form. My intuition tells me that since a constant is not a vector, it would only be multiplying with a vector when in a cross product with one. Since the vector will only grow larger in magnitude, there would be zero area in the paralleogram formed because there is no paralleogram.

2. ### micromass

19,347
Staff Emeritus
The cross product is only defined between vectors of $\mathbb{R}^3$. The cross of a constant and a vector is not defined.

3. ### quantumfoam

127
So if I had an equation that contains a term that has a cross product of a constant and a vector, do I just cross it out of the equation? ( it is in an adding term so crossing it out would be okay). That's an awesome joke(:

4. ### micromass

19,347
Staff Emeritus
Can you give a specific example?

5. ### quantumfoam

127
Sure! An equation like F=π[hXh+cXh] where h is a vector and c is a constant.

Last edited: Jan 31, 2013
6. ### micromass

19,347
Staff Emeritus
That doesn't really make any sense.

7. ### quantumfoam

127
F is a vector.

127

9. ### quantumfoam

127
Would the term containing the cross product of the constant c and vector h in the above equation just be zero? Or am I able to take cross it out of the above equation?

10. ### micromass

19,347
Staff Emeritus
No. As it stands, your equation makes no sense. You can't take the cross product of a scalar and a vector.

11. ### quantumfoam

127
Damn that stinks. Even if the c was a constant?

12. ### micromass

19,347
Staff Emeritus
Does this equation appear in some book or anything? Can you provide some more context?

13. ### quantumfoam

127
Well I made it up haha. Im sorry. I'm new at this. Do you think you can make an equation that makes sense? Like the one I attempted but failed at.

14. ### micromass

19,347
Staff Emeritus
It only makes sense if you take the cross of a vector and a vector.

What were you attempting to do?? What lead you to this particular equation?

15. ### quantumfoam

127
Well, the h is a vector that represents a magnetic field strength. In the definition of a current, I=dq/dt, multiplying both sides by a small length ds would give the magnetic field produced my a moving charge. (dq/dt)ds turns into dq(ds/dt) which turns into vdq where dq is a small piece of charge and v is the velocity of the total charge. Integrating both sides to I ds=vdq would give the total magnetic field. For a constant velocity, the right side of the above equation turns into vq+ c, where c is some constant. Now I get the equation h=vq+c. Solving for qv gives me h-c=qv. In the equation for magnetic force on a moving charge, F=qvxB. I substituted h-c for qv in the above force equation. B turns into uh where u is the permeability of free space. I substitute uh for B in the magnetic force equation and get F=u[hxh-cxh]. I want the cxh term to go away.

16. ### quantumfoam

127
Does that sort of help?

17. ### micromass

19,347
Staff Emeritus
I don't understand any of what you said, but my physics is very bad. I'll move this to the physics section for you.

18. ### quantumfoam

127
Thank you very much!(:

19. ### HallsofIvy

40,769
Staff Emeritus
Saying that c is a 'constant' doesn't mean it is not a vector. A "constant" is simply something that does not change as some variable, perhaps time or a space variable, changes. In your formua c is a constant vector.

20. ### quantumfoam

127
Ohhh. That makes a lot of sense! Is there anyway I could determine what the constant vector is?