]> 3.2 Rotating Coordinates in a Euclidean Space

3.2 Rotating Coordinates in a Euclidean Space

If we rotate basis vectors i ' ^ and j ' ^ by angle θ 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 θ + v j sin θ

and v j becomes

v j ' = v i sin θ + v j cos θ

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