question_answer

If \[\vec{A}\times \vec{B}=\vec{C}\times \vec{B},\] show that \[\vec{C}\] need not be equal to \[\vec{A}\] .

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               \[(\vec{A}-\vec{C})||\vec{B}.\]