# Multivariable Calculus Vector Fields

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.

• Sorry, meant to say prove that it is also conservative just for clarification. – user126006 Feb 4 '14 at 2:57
• 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 $cf+dg$. – Ted Shifrin Feb 4 '14 at 3:09