Question

Vector A has the magnitude of 12 m and is angled 60 degrees counterclockwise from the positive direction of the x axis of an xy plane. Also vector b = 12i + 8j on that same corrdinate system. We now rotate the system counterclockwise about the orgin by 20 degrees to form a new system. On this new system what are (a) vector A and vector B both in unit-vector notation?

I couldn't figure out what I should do to solve this problem.


Change vector B to polar (magnitude at some angle). I think this will be 14.4 at 33.7 degrees counterclockwise from the x axis. Check that. Now, sketch the system, including the new axis. On the new system, you have
A'=12@(60-20) and B'=14.4@(33.7-20)
Convert those to the new i,j system ...

A'=12'cos40+ 12j'sin40 check that, and convert the B'

I will be happy to check your work.

If you are a college student, there is another way of rotating axis and vector systems, in vector form. Check your text on that.
http://www.nytimes.com/2006/10/06/us/06evangelical.html?_r=1&ref=us&oref=slogin