3
$\begingroup$

I have to prove that if $f(x,y,z)=f_{a}(x,y,z)+f_b(x,y,z)+f_c(x,y,z)$ is a conservative vector field and and $g(x,y,z)=g_{a}(x,y,z)+g_b(x,y,z)+g_c(x,y,z)$ is also a conservative vector field, then $(cf+dg)(x,y,z)$ is conservative.

$\endgroup$
  • $\begingroup$ Sorry, meant to say prove that it is also conservative just for clarification. $\endgroup$ – user126006 Feb 4 '14 at 2:57
  • 2
    $\begingroup$ While you're editing, do you mean $f = (f_a,f_b,f_c)$? These should be vector-valued functions. Here's a hint: What does conservative mean? Write that down for each of $f$ and $g$ and see if you can deduce what you want for $cf+dg$. $\endgroup$ – Ted Shifrin Feb 4 '14 at 3:09
0
$\begingroup$

I think that if they are real valued functions it would change the nature of the answer because then I think it becomes a proof of curl(f)+curl(g)=curl(f+g), which is easy enough to prove.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.