Strafe

To look around in my world I use gluLookAt(). I can to all kinds of movement except strafe. My ideia is: I have 3 points (used in gluLookAt), get the general plane equation from those points and I get a normal to that plane. Now I just sum that to my origim, and that’s that!
Is this the best way to do this? Is there any other? Thanks…