1. The problem statement, all variables and given/known data A defining property of a vector is that its components must transform in a particular fashio under a rotation. for a counterclockwise rotation around the z-axis, by and angle ∅ the components Ax, Ay, and Az of a vector A transform in the following fashion: Ax --> Ax' = Axcos∅ + Aysin∅ Ay --> Ay' = -Axsin∅ + Aycos∅ Az --> Az' = Az Show that the cross product A x B acts as a vector under a rotation about the z-axis 2. Relevant equations see above 3. The attempt at a solution i think what i am having trouble is knowing what i am aiming to show. so i have started out rather blindly, setting up some conditions and hoping that it will show me some clue. i rotated the coordinate system for A and B until A sits directly along the positive X-Axis and B lies above it pointed up in the positive Z direction, diverging by an angle ∅. i was looking at A being rotated 90 degrees counterclockwise Ax = A Ay = 0 Az = 0 Bx = Bcos∅ By = 0 Bz = Bsin∅ this gave me a cross product of --> -ABsin∅ along the Y-axis this didn't tell me anything i am assuming that AxB is to be likened to a transformation of A but i am unsure how to proceed [am i supposed to be placing AxB straight up in the z-axis?