If AxB = CxB , show that C need not be equal to A , where A, B , C are vectors . ??

                AxB = CxB

Implies     |A| |B| sin Θ = |C| |B| sin Φ  

(where Θ: angle between vector A and B; Φ: angle between C and B)

 

|A|  sin Θ = |C| sin Φ

If   Θ = Φ, then A = C, else not.

 

Hence proved that C need not be equal to A.