A) \[\frac{\sqrt{3}}{2}\left| \text{A} \right|\]
B) |A|
C) \[\frac{\sqrt{2}}{2}\left| \text{A} \right|\]
D) \[\sqrt{3}\]|A|
Correct Answer: D
Solution :
\[{{\left| A+B \right|}^{2}}={{\left| A \right|}^{2}}+{{\left| B \right|}^{2}}+2AB\Rightarrow 2AB={{\left| A \right|}^{2}}\] or \[-2AB={{\left| A \right|}^{2}}\] \[\left[ \left| A+B \right|=\left| A \right|=\left| B \right| \right]\] \[\therefore {{\left| A-B \right|}^{2}}={{\left| A \right|}^{2}}+{{\left| A \right|}^{2}}+{{\left| A \right|}^{2}}=3{{\left| A \right|}^{2}}\]
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