The problem shown in the image is from MIT OCW. The problem asked to calculate the flux of the force, $F = -x\hat i + x\hat k$ through the surface, $z = x^2 + y$. According to the solution shown, $F$ is the vector $(−y, x, 0)^T$. I thought F should be $(-y, 0, x)^T$. Am I wrong?
problem:
You’re correct, in Step 2 and onward they switched to $\mathbf{F} = -y \mathbf{i} + x \mathbf{j}$