3.2 Rotating Coordinates in a Euclidean Space

If we rotate basis vectors i' and j' by angle from i and j, (so that the i' direction rotates toward j) the components of a fixed vector v change as follows:

v_i becomes

v_i' = v_i cos +  v_j sin

and v_j becomes

v_j' = - v_i sin + v_j cos

These effects are illustrated in the accompanying applet. You can move the vectors and also rotate the basis.