Consider a rotation about an axis $=\frac{\left[\begin{array}{ccc}2& 3& 4\end{array}\right]}{{\left[\begin{array}{ccc}2& 3& 4\end{array}\right]}^{TT}}|{|}^{TT}$ by an angle $=45.$

a$.$ Using Matlab, compute $e^{\text{h}\text{a}\text{t}()}$ by applying Rodrigues' formula $($you may use the hat func$-$

tion you wrote in problem $1).5$ pts$.$

b$.$ Now use the Matlab command expm to evaluate $e^{\text{h}\text{a}\text{t}()},$ and verify that the results are the

same. Note that typically when finding forward kinematics by the product of exponen$-$

tials method, it is possible to use the expm function rather than evaluating Rodrigues'

formula explicitly. $5$ pts $.$

c$.$ Use two key properties of rotation matrices to verify that the $33$ matrix you found in

parts a and b is a rotation matrix. $5$ pts $.$