3DTransformation

[causs]

Hi there,
I am trying to figure out an algorithm to transform the unit vectors of a world coordinate-system after It is rotated by the angle a,b,c along Z-axis, Y-axis and X-axis, in turn or It migt be in any order which means a lot of complication. After some Linear Algebra, It  seems It is more than some matrix multiplication. Has any one have any idea how to handle this issue? Any clue for a sample code or tutorial is deeply appreciated.
Thanks in advance.