Need help for a prove about magnetic field and magnetic force

1. Oct 13, 2004

humanallien

here is the problem:

prove that the vector of the magnetic force cannot be parallel to the plane that contains the vector of the particle's velocity and magnetic field.

2. Oct 13, 2004

Tide

By definition of cross product you have both

$$\vec v \cdot \vec v \times \vec B = 0$$

and

$$\vec B \cdot \vec v \times \vec B = 0$$

which say that both $\vec v$ and $\vec B$ are perpendicular to $\vec F = \vec v \times \vec B$.

3. Oct 13, 2004

humanallien

thanks for your advice, but it does not help me with the problem because I have to assume that I do not know the definition of F = v X B for the prove. Therefore, I want to proof that the force vector is NOT parallel to the plane without considering the definition of the croos product

4. Oct 13, 2004

Tide

Since the fundamental behavior of charged particles interacting with a magnetic field comes only from observation (Thomson, Lorentz, etc.) it would seem unlikely that you could "prove" the result by other means. It would be like attempting to prove the electric force on a charged particle acts parallel to the electric field - without invoking Coulomb's Law. Good luck!