calculus and analysis – Picking elements from separate lists and multiplying them

So I’m doing some instruction items about surface integrals. I’ve written the following code. it calculates curl and partial derivatives of the surface. I now want to create the following function, which will be my integrand. Merely dot producting the two vectors doesn’t change the signs like I need. Is there a way to says multiply one element of a vector times its corresponding one and changing the sign, along the way?

What I want to do is change the sign of the first two elements created by the dot product, whle leaving the third alone.

Here’s my code;

F = {2 z, 4 x, 5 y};
Print("The curl is:")
NewF = Curl(F, {x, y, z}) (*Step 1*)

g = x + 4;(*Step 3 solving for z of the curve*)
Print("The partial derivatives of z are the following (with 1 as a placeholder for R):")
g1 = {D(g, x), D(g, y), 1}(*Step 4, the partials of z*)
Print("The new integrand is the following (don't forget to sub g for z.")
NewF . g1

The curl is shown to be 5,2,4 and the partials are 1,0,1. But a correct answer for what i want to do gives 1 as the ‘new integrand’ while the code here gives ‘9.”

Any thoughts?