Random number generation with equal length

I would like to generate random n-dimensional points with the same distance from the origin. i.e. norm(point) should be equal for all points... how can i achieve this?

Answer 1

[John D'Errico]

In n dimensions, to generate 1 such point...

X = randn(1,n);
X = X./norm(X);

To generate many such points, it is as easy a generating an array, then dividing each row by the norm of that row. sum and bsxfun will be of help here.