Right Hand Rules in Physics: Is There a Way Around It?

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Pseudo Statistic
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Hey,
We recently started learning about magnetic fields and forces in physics and we took these weird right hand rules...
After much attempt I cannot, for the life of me, figure them out.
Is there any way I can find the direction of the field or a force without using my right hand? Like on paper or mathematically or something? (Choosing "approximate directions" ofcourse)
Thanks for any responses.
 
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The right-hand rule is a mnemonic for the cross product. The algebra of the cross product is already oriented.
However, for quick reference, you should just use your right hand.
 
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Be sure to check out these http://physics.syr.edu/courses/video/RightHandRule/index2.html" .
 
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