The temperature at a point $(x,y,z)$ is given by $T(x,y,z)=100e^{-x^2-3y^2-7z^2}$ where $T$ is measured in $C$ and $x,y,z$ in meters.

$($a$)(12$ pts$.)$ Find the rate of change of temperature $($in $\frac{C}{m})$ at the point $)$ in the direction to point $Q(1,3,2).$

$($b$)(4$ pts$.)$ In which direction does the temperature decrease fastest at $P?$