Why is a small change in an angle considered vector?

Question

Why is a small change in an angle considered  vector?

experimentx · Answer

can you elaborate?

dls · Answer

no,ive just heard that line :/

anonymous · Answer

Angle insinuates there is a direction. Anything with a direction is a vector quantity

anonymous · Answer

ANY change in the angle is a vector because it changes the direction..

dls · Answer

Can you ellaborate?

dls · Answer

@pavaneinstine ?

anonymous · Answer

wat is there to elaborate?o.O

dls · Answer

ANY change in the angle is a vector because it changes the direction..
why is it a vector..a little more detail?

anonymous · Answer

vector is a quantity which has magnitude and direction.. so change in angle which has both.. is a vector

dls · Answer

so why isnt "angle" not change  a vector?

dls · Answer

no direction?

anonymous · Answer

because it doent hav a direction.. :) if i say 2 degrees.. u dont hav a clue abt whih direction..

dls · Answer

alright!

experimentx · Answer

do you mean $ d \theta $ or $ \hat \theta $

dls · Answer

former

experimentx · Answer

a vector should be something like this 
$$ d \vec r$$
you know this is change in position vector. dr is just magnitude.

dls · Answer

then latter :P

experimentx · Answer

$ \huge  {d\vec r  \over d \theta } = \hat \theta $  I'm not sure if $ d\theta $ is a vector. most probably not!!

dls · Answer

wait what,
don't confuse!

fwizbang · Answer

It has to do with the properties of the rotation matrices when the angles are 
infinitesimally small. When you apply two such rotations, the product of the two matrices is the same matrix as the matrix that you'd get first adding the 
rotations like a vector.