(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Rotation around the z-axis and cross products

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