in two dimensions, consider the orthogonal x-y axis pair with the associated unit vectors i and j.
Suppose we rotate these axes about the origin by an angle , in the counterclockwise direction, and
rename them as the x'-y'-axis coordinates system with the associated unit vectors i' and j'
(a) Write the unit vectors i and j in terms of i' and j'.Express your results in terms of sintheta and costheta .
(b) Suppose V = i + 9 j. Rewrite V in terms of i' and j'.
(c) Finally, suppose V = i + 9 j, and tan = 9. Rewrite V in terms of i' and j'

Question

in two dimensions, consider the orthogonal x-y axis pair with the associated unit vectors i and j.
Suppose we rotate these axes about the origin by an angle , in the counterclockwise direction, and
rename them as the x'-y'-axis coordinates system with the associated unit vectors i' and j'
(a) Write the unit vectors i and j in terms of i' and j'.Express your results in terms of sintheta  and costheta .
(b) Suppose V = i + 9 j. Rewrite V in terms of i' and j'.
(c) Finally, suppose V = i + 9 j, and tan  = 9. Rewrite V in terms of i' and j'