hi, any help with proving that grad (v_ . r_) = v_ using spherical polars, where v_ is a uniform vector field would be great
it is trivial to prove using summation convention or cartesian coordinates but having to use spherical polars looks messy...
The Attempt at a Solution
i know the identity: grad (a_.b_) = a x curl b + b x curl a + a . grad b + b . grad a
is it true that curl v_ and grad v_ are 0 since v_ is a uniform field? and grad r_ is the unit vector of r_? and curl r_ is 0? where i think r_ is the position vector...