Calculating an average vector

Hi,

Given a set of N vectors, how can I calculate the average vector of the
set. An average vector is defined (at least for the problem at hand) as a
vector which have a magnitude in the range of min-max magnitude of the
set, and have the average direction of the set.

From what I know about vectors, the total sum of the set will give the
average direction.

Because I don't want the magnitude of a vector to contribute to the
average direction, the steps I have already took are:

1. calculate the unit vectors for each vector in the set
2. get the total of those unit vectors
3. calculate the unit vector of that total
4. calculate the average magnitude of the set
5. take the direction vector of step #3 and magnitude of step #4 to
create the final vector

if the unit vector of step #3 is given by: a.i + b.j+ c.k
and the magnitude of step #4 is given by M
then the final vector of step #5 is given by (M*a)i + (M*b)j + (M*c)k

The problem is how to make the average vector have a magnitude in the
range of the min-max magnitude of the set. I'm not sure the steps I have
taken is appropriate, and whether it can be generalized to vectors with
any dimensions (I'm thinking of 6 or more dimensions).

TIA
.

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