I have this question. My bird is is in this point: (1,1,3) in 3D, and the source of the radiation is in that point too.
What is the direction for her to fly from that point, if it wants to minimize the radiation the quickest way?
The radiation expressed by:$$ R(x,y,z) = 1/((x-1)^2+(y-1)^2+(z-3)^2 + 1) $$
The gradient is (0,0,0) at this point, what is predictable, because in that point we have the max radiation (easy to see). If I understand correctly, this kind of exercizes we solve this way: 1. Find the gradient 2. If there arent any restrictions on the object, the maximal directions is the direction of the gradient (and the mminimal is minus the gradient) 3. If there are restrictions, for example we are talking about a reptile, that cant fly any directions, but can only move above the surface, we need to find the N and do Gradint dot N = 0 and find the missing component (but in our case its not relevant).
So what do i do if the gradient is 0, as in this case ? Does it mean that any direction is good enough to minimize most quickly the radiation ? Or did I miss something ?
By symmetry, every direction is equivalent.