question_answer 42)

                  It is found that \[|\vec{A}+\vec{B}|\,=\,|\vec{A}|\]. This necessarily implies.                 (a) B = 0                 (b) A, B are antiparallel                  (c) A, B are perpendicular                 (d) A.B \[\le \] 0 

Answer:

                  (b) \[|\vec{A}+\,\vec{B}|\,\,=\,|\vec{A}{{|}^{2}}\Rightarrow \,(\vec{A}+\vec{B})\,.\,(\vec{A}+\vec{B})\,=\vec{A}\,.\,\vec{A}\]                 \[\therefore \,\theta ={{180}^{o}}\]