question_answer

Two vectors \[\vec{A}\] and \[\vec{B}\]are added. Prove that the magnitude of the resultant vector cannot be greater than(A + B) and smaller than (A - B) or (B - A).

Answer:

                Yes. Given \[\vec{A}+\,\vec{B}+\vec{C}+\vec{D}=\vec{0}\] or \[\vec{A}+\,\vec{B}+\vec{C}=\vec{0}-\vec{D}=-\vec{D}\] Hence magnitude of \[(\vec{A}+\,\vec{B}+\vec{C})\]must be equal to the magnitude of \[\vec{D}\].