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If a vector A having a magnitude of 8 is added to a vector B which lies along X-axis, then the resultant oftwo vectors lies along Y-axis and has magnitude twice that of B, The magnitude of B is

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a

65

b

125

c

165

d

85

answer is D.

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Detailed Solution

According to given condition,A+ Bi^ = Rj^ (where, R is the resultant vector)Also, R = 2B∴ ∣A+Bi^=2Bj^ or A=2Bj^-Bi^∴ A2 = 4B2 + B2 = 5B2Here, A = 8∴ 64 = 5B2⇒ B=645=85

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