The vectors , , and are given, with respect to an orthonormal
basis , by
- (a) Evaluate .
- (b) Evaluate . Is a tensor? If not, why not? If yes, what is the order of the tensor?
- (c) Name and define and .
- (d) Evaluate .
- (e) Show that .
- (f) Rotate the basis by 30 degrees in the counterclockwise direction around to obtain a new basis . Find the components of the vector in the new basis .
- (g) Find the component of in the new basis .
Because cannot be an even or odd permutation of .
The basis transformation rule for vectors is
The basis transformation rule for second-order tensors is