How to find the resultant vector of a matrix?

Consider a matrix(m) as

m = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

I define the vectors as

Clearly, there are 8 vectors and all pointing towards 5. The angle between any two consecutive vectors is 2 Pi/8 = Pi/4. The magnitude of each vector is defined as the difference between the central value (5 in this case) and the value corresponding to the other element.

Therefore,

vector 1 has a magnitude of |(5-1)|=4 and direction 7 Pi/4,

vector 2 has a magnitude of |(5-2)|=3 and direction 3Pi/2,

vector 3 has a magnitude of |(5-3)|=2 and direction 5Pi/4,

vector 4 has a magnitude of |(5-6)|=1 and direction Pi,

vector 5 has a magnitude of |(5-9)|=4 and direction 3Pi/4,

vector 6 has a magnitude of |(5-8)|=3 and direction Pi/2,

vector 7 has a magnitude of |(5-7)|=2 and direction Pi/4,

vector 8 has a magnitude of |(5-4)|=1 and direction 0,

Under the given construction how can I efficiently calculate the resultant vector?

[I want a generalized solution for this so that it can be applied for any length of m. ]