Prove that if is the angle between u and v and u . v =/= 0, then tan = ||u x v||/(u . v)
where . is dot product
I am pretty familiar with the properties of both dot and cross product but that tan throws me for a loop, I just can't seem to find a way to do this
Thanks for the speedy reply!
I'm not sure if this is too basic, or only physics related or something but I guess that means to use SOH CAH TOA, where O = || a x b ||, and A = a . b
Therefore tan = || a x b || / a . b
and ah! that turns out to be the given answer!
now to prove it... I see that u . v =/= 0, which means that u and v are not orthogonal.. That's all I really can come to right now, I haven't had much luck with the geometric interpretation
Edit: Or am I complicating this, and simply showing the explanation of sin and cos to tan would be sufficient?