A) \[90{}^\circ \]
B) \[60{}^\circ \]
C) \[75{}^\circ \]
D) \[45{}^\circ \]
Correct Answer: A
Solution :
As we have given \[|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|\] or \[\sqrt{{{A}^{2}}+{{B}^{2}}+2AB\cos \theta }\] \[=\sqrt{{{A}^{2}}+{{B}^{2}}-2AB\,\cos \theta }\] where \[\theta \] is the angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\]. Squaring both sides, we have \[{{A}^{2}}+{{B}^{2}}+2\,AB\,\cos \theta ={{A}^{2}}+{{B}^{2}}-2AB\,\cos \theta \] or \[4AB\,\,\cos \theta =0\] As \[AB\ne 0\] \[\therefore \] \[\cos \theta =0-\cos {{90}^{o}}\] \[\therefore \] \[\theta ={{90}^{o}}\] Hence, angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is 90°.You need to login to perform this action.
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