Suppose That the Temperature at the Point $( x , y , z )$

Multiple Choice

Suppose that the temperature at the point $( x , y , z )$ is given by $T ( x , y , z ) = e ^ { - z ^ { 2 } } \sin ( x y )$ .If you are at the point $( 1,2 \pi , 0 )$ , in which direction should you go to decrease your temperature the fastest?

A) $2 \pi \vec { i } + \vec { j } + 0 \vec { k }$
B) $2 \pi \vec { i } - \vec { j } + 0 \vec { k }$
C) $2 \pi \vec { i } + \vec { j } - \vec { k }$
D) $- 2 \pi \vec { i } - \vec { j } + 0 \vec { k }$
E) None of the above; the gradient of T is zero at $( 1,2 \pi , 0 )$ .