I have a question that's puzzled me for some time. Can anyone explain?

Will the normalized vector(1,1,1) and the vector(1,0,0) that's been rotated around the y-axis pi/4 rad and then pi/4 rad around it's own x-axis have the same value in it's x, y and z components?

(That is if you rotate in the right directions though I don't know which they are)