A) 1
B) 2
C) 3
D) None of these
Correct Answer: A
Solution :
\[(\overrightarrow{A}+\overrightarrow{B})\] is perpendicular to \[(\overrightarrow{A}-\overrightarrow{B})\]. Thus \[(\overrightarrow{A}+\overrightarrow{B})\].\[(\overrightarrow{A}-\overrightarrow{B})\] = 0 or \[{{A}^{2}}+\overrightarrow{B}\,.\,\overrightarrow{A}-\overrightarrow{A}\,.\,\overrightarrow{B}-{{B}^{2}}=0\,\] Because of commutative property of dot product \[\overrightarrow{A}.\overrightarrow{B}=\overrightarrow{B}.\overrightarrow{A}\] \[\therefore \]\[{{A}^{2}}-{{B}^{2}}=0\] or \[A=B\] Thus the ratio of magnitudes A/B = 1
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