A) \[\frac{6}{\sqrt{5}}\]
B) \[\frac{12}{\sqrt{5}}\]
C) \[\frac{16}{\sqrt{5}}\]
D) \[\frac{8}{\sqrt{5}}\]
Correct Answer: D
Solution :
According to condition \[\mathbf{A+Bi=Rj}\] (where, \[\mathbf{R}\] is the resultant vector) Also, \[\mathbf{R}=2\mathbf{B}\] \[\therefore \] \[\mathbf{A+Bi=2Bj}\] or \[\mathbf{A=2Bj-Bi}\] \[{{A}^{2}}=4{{B}^{2}}+{{B}^{2}}=5{{B}^{2}}\] Here, \[A=8\] \[\therefore \] \[64=5{{B}^{2}}\] \[\Rightarrow \] \[B=\sqrt{\frac{64}{5}}=\frac{8}{\sqrt{5}}\]
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