Question

prove the relation V=W X R​

Answer 1

How to derive the formula:

v=wr where v is the tangential velocity, w is the rotational velocity, and r i the radius vector? From the attached image, it can be concluded that (each quantity is a vector): w=r x v, also v=w x r, and r= v x w. All three vectors are perpendicular to each other, therefore the intensity of each vector can be calculated by vector multiplication. Then (each quantity is a vector modulus): w=rv, v=wr, r=vw, this system of equations is true if w=v=r which mustn't be true. I need an explanation. What did I wrong to arrive at this incorrect equality?