Suppose $\hat r$ is an position operator, $\hat p$ is a momentum operator and $\vec c$ is a constant vector.
What does the commutator $[\hat p, \vec c\cdot\hat r]$ mean?
I see that you can expand the second term such that the commutator becomes $[\hat p, c_xr_x+c_yr_y+c_zr_z]$ but then one of the operators in the commutator is a "vector" whereas the other is a scalar? Perhaps I am interpreting this wrong.
What would the value of $[\hat p, \vec c\cdot\hat r]$ be? Given that $[x,p_x]=i\hbar$? where $x$ is a component of $\hat r$ and $p_x$ the corresponding component in $\hat p$.