(Solved): 1. Use abbreviated index notation to evaluate the following expressions involving the position vec ...

1. Use abbreviated index notation to evaluate the following expressions involving the position vector \( \boldsymbol{x} \) in a Cartesian coordinate system (where \( |\boldsymbol{x}|=r \) ) and arbitrary vector \( \boldsymbol{u} \). a. \( \nabla \cdot \boldsymbol{x} \) b. \( \nabla \wedge \boldsymbol{x} \) c. \( \nabla^{2}\left(\frac{1}{r}\right) \) d. \( \nabla \wedge \nabla \boldsymbol{u} \) e. \( \nabla \cdot(\nabla \wedge \boldsymbol{u}) \)