$($B$2)$ The temperature at the point $(x,y,z)$ is given by $T(x,y,z)=200e^{-x^2-3y^2-9z^2},$ where $T$ is measured in $C$ and $x,y,z$ in meters.

a$.[8$ pts$]$ Find the exact rate of change of the temperature at the point $P(2,1,-2)$ in the direction of the point $Q(3,3,-3).$ Include units in your answer.

b$.[2$ pts$]$ Get a decimal approximation in scientific notation of the answer you got in part a to write a simple sentence to interpret what your answer means in this context. Be specific and clear.