Let f : r 3 → r be a scalar function and let f be a vector field in r 3 . assume that all derivatives exist and are continuous at all points. for each expression below, state whether it is

(a) not meaningful (i. e., not defined);
(b) a scalar function which is identically zero;
(c) a scalar function which is not necessarily identically zero;
(d) a vector field which is identically zero; or
(e) a vector field which is not necessarily identically zero. you do not have to justify your answers. (grad = gradient.)