Velocity of a bee moving along the curve of intersection of 2 surfaces

[karokr94]

Hi, I've attached the problem and the solution. I understand the solution except for one thing. I've circled the part I'm having problems with. How do I decide if the circled part should be
f₂(x,y,z)=x²-y²-z or
f₂(x,y,z)=z-x²+y²

I'm sure it has something to do with the fact that the problem statement states that the bee is moving in the increasing direction of z, but I just can't figure out how it translates into f₂ being one or the other. Or are both answers acceptable?

Thanks in advance for the help!

 

[karokr94]

Never mind, I figured it out.