How can I create random Co-ordinate shifts (x,y,z) that add to a displacement of 1?

I have a set of co-ordiantes with x, y and z values. I'm trying to shift the co-ordiantes randomly to produce an overall shift of 1 (mm).

I know that if i'm shifting x y and z by random amounts of a b and c respectively, then:

sqrt(a^2 + b^2 + c^2) = 1

How can I randomly produce a vector (a, b, c) that satisfies the above equation?

Thanks!!

Answer 1

[Matt J]

[a,b,c]=sph2cart(2*pi*rand,pi*rand,1);

[Hannah Taylor]

wow, thank you!