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:

vi becomes

vi' = vi cos + vj sin

and vj becomes

vj' = - vi sin + vj cos

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