Motion of Charged Particles in Field Uniform B-field E=0

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Hello!

So I've been working on proving to myself different parts of https://ocw.mit.edu/courses/nuclear...a-physics-i-fall-2003/lecture-notes/chap2.pdf packet for several weeks.

Under 2.1 Uniform B field, E=0, for the Larmor Radius, I need to know perpendicular v, but I want to figure it out in terms of anything except rL and omega.


I'm especially wondering what "perpendicular velocity" would mean and how to find it. I was thinking about cross products and dot products, but what would I cross with the velocity? I also don't know any angles, because right now I have no data- I'm just trying to do theoretical and trying to avoid angles.

It's late at night, thank you for helping me!
 
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Hi! I also wanted to say that I'm in AP Calculus right now, and in Physics C AP. This is for my science research project, so I'm willing to put in the time and effort to learn math/physics that I don't know yet, although I am in a really big time crunch.