If (¯¯¯aׯ¯b)2+(¯¯¯a⋅¯¯b)2=144 and |a|=4, then |b| is equal to
A
16
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B
8
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C
3
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D
12
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Solution
The correct option is D3 Since, (¯¯¯aׯ¯b)2+(¯¯¯a.¯¯b)2=144 If angle between ¯¯¯a and ¯¯b is θ. then |a|2|b|2sin2θ+|a|2|b|2cos2θ=144 ⇒|¯¯¯a|2|¯¯b|2=144 ⇒|¯¯¯a||¯¯b|=12 ⇒4|¯¯b|=12 ⇒|¯¯b|=3