Showing Lorentz force and velocity are perpendicular with constant magnitudes

[jlmac2001]

The force acting on a moving charge particle with mass m and charge q in a magnetic field B is the Lorentz force F= q(v x B), where v is it's velocity. Suppose thata particle moves in the (x,y) plane with a uniform B field in the z direction. Assuming Newton' second law, mdv/dt = F, show that the forceand velocity are perpendicular, and that both have constan magnitude. Hint: Find (d/dt)(v dot v).


I don't know where to start. How do you take the derivative of v dot v?

 

[Hurkyl]

Use the product rule:

$$\frac{d}{dx}( f \cdot g ) = f \cdot \frac{dg}{dx} + \frac{df}{dx} \cdot g$$

 

[jlmac2001]

still don't get it

Can you elaborate? I don't understand.