All the problems are from the course text, Craig, Introduction to Robotics. Unless otherwise indicated, each problem is worth 10 points.

1. 2.3
2. 2.5
3. 2.14
   Hint: see Example 2.9.
4. 2.20
   Hint: let K = (K_x, K_y, K_z)^T and Q = (Q_x, Q_y, Q_z)^T and simply expand Rodruques' formula to verify that it is the same as the matrix given in Equation 2.80 multiplied by Q.
5. 2.23
6. 2.35
7. 2.38
   Hint: use the matrix multiplication representation of the dot product and the fact that the angle between the two vectors remains fixed.