question_answer 52)

                  \[\vec{A},\,\,\vec{B}\] and \[\vec{C}\] are three non-collinear, non vectors. What can you say about direction of \[\vec{A}\times \,(\vec{B}\times \,\vec{C})\]?

Answer:

                  \[\vec{B}\times \,\vec{C}\,\] is perpendicular to the plane containing \[\vec{B}\] and \[\vec{C}\] i.e. it is along z-axis. Then \[\vec{A}\,\times \,(\vec{B}\times \,\vec{C})\] is perpendicular to z-axis. Hence, \[\vec{A}\,\times \,(\vec{B}\times \,\vec{C})\] is in the plane of \[\vec{B}\] and \[\vec{C}\].