I'm working on problem 2. Trying to prove that the dot product between a vector field and its curl is zero.
The basic identities of vector calculus and how scalar fields and vector fields interact
The Attempt at a Solution
My only real attempt is expanding what was given using an identity. What i have now is that
f(del X A) = A X del(f)
In my head the proof is trivial since by the very definition of the cross product, the new vector while be perpendicular to both vectors that served as the argument. I do have a question though. In the above notation and in the identity when they say f(del X A) do they mean to input the curl vector as an argument for the scalar function? Thanks!