directional unit vector

[SigepBrandon]

Thanks for all the help and people that have responded to my other posts thus far.

The exercise reads:
The temperature at the point (x,y,z) in space is given by T(x,y,z)= x + yx. A fly is at the point (1,2,1). In what direction should he begin to fly to cool off as quickly as possible? Your answer should be a unit vector in the requested direction.

Question:
Wouldn't the solution just be the unit vector of \(\displaystyle \nabla\)f(1,2,1)?

I've already completed the computation, just wanted to verify my thought-

 

[SigepBrandon]

if you'd like to verify:

\(\displaystyle T(x,y,z)=x+yz\) Point (p)= (1,2,1)

\(\displaystyle \nabla\)f = <1,z,y>
\(\displaystyle \nabla\)f(1,2,1)= <1,1,2>
Magnatude of \(\displaystyle \nabla\)f(1,2,1) = 2*sqrt(3)
Unit vector u = <(1/(2*sqrt(3))),(1/(2*sqrt(3))),(1/(sqrt(3)))>

or- maybe I'm missing something?