Answer:
As \[\vec{A}\times \vec{B}=\vec{C}\times \vec{B}\] \[\therefore \] \[\vec{A}\times \vec{B}-\vec{C}\times \vec{B}=0\] or \[(\vec{A}-\vec{C})\times \vec{B}=0\] This implies that if \[\vec{C}\ne \vec{A},\] then either\[\vec{B}=\vec{0}\] or \[(\vec{A}-\vec{C})||\vec{B}.\]
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