Suppose I have a vector A on the 2d co ordinate system x and y and therefore vector A = Axi + Ayj where i and j are unit vectors along x and y axis.

Suppose a new co ordinate system is introduced in which is x'y' and is titlted from the xy plane by angle theta and both the co ordinate systems (xy and x'y') share the same origin.

The component of the vector seem to change on x'y' plane.

A = i'Ax' + j'Ay' (i' and j' are the unit vectors along the x' and y')

and now i' = i cos (theta) + j sin (theta)

j' = - i sin (theta) + j cos (theta)

Kindly help me understand the concept.