My question is about directional derivatives that i could not understand completely...
The heat function on every point of a plane is given as T(x,y,z) = xyz and also the point t = (1,1,1) is given. Starting from the point t, in which direction we go the heat does not change?
The derivative in a point $p = (1,1,1)$ is the vector $D_pT = (\partial_xT, \partial_yT, \partial_zT, )$. Now the value of $T$ does not change in the direction of the vector $v$ for which $D_pT \cdot v = 0$
The rest is just calculation. Btw "heat" function is a bit misleading, because your function $T$ does not really resemble something heat-like.
