Find the angle between two coordinate systems.

Question

Hi, I need to find out the angle between the two vectors $x$ and $x'$ based on the two angles $\alpha$ and $\alpha'$, also the points $A$ and $O'$ are known in both coordinate systems $(O,x,y)$ and $(O',x',y')$. Basically I need to find out the angle between the two coordinate systems. Note that $OA$ and $x'$ are not parallel. Thank you in advance for your answers and don't hesitate to ask for further details.

Answer 1

From

$$OA=OO'+O'A\implies O'A=OA-OO'$$

we can find O'A in the system (O,x,y) and then find its angle with x axis.

We can also can find the angle of O'A in the system (O',x',y').

Thus by the difference we can find the angle between x and x'.