Problem 2B17 (page 71)

Problem:

   The basis is obtained by a counterclockwise rotation of the   basis about   

(a)     Find the orthogonal transformation Q that defines this change of basis, i.e.

(b)      By using the vector transformation law, find the components of    in the primed basis (i.e., find )

Solutions:

(a)

 

(b)

(c)

Clearly, is a vector in the same direction as and has length of 2.