6. (B2) 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.
