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Question

If |¯¯¯a|=1,|¯¯b|=2,|¯¯¯a¯¯b|2+|¯¯¯a+2¯¯b|2=20, then (¯¯¯a,¯¯b)=

A
π3
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B
π4
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C
π6
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D
2π3
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Solution

The correct option is B 2π3
Given
|¯a|=1,|¯b|=2,|¯a¯b|2+|¯a+2¯b|2=20

|¯a|2+|¯b|22|¯a||¯b|cos(¯a,¯b)+|¯a|2+4|¯b|2+4|¯a||¯b|cos(¯a,¯b)=20

2|¯a|2+5|¯b|2+2|¯a||¯b|cos(¯a,¯b)=20

2(1)2+5(2)2+2×1×2×cos(¯a,¯b)=20

22+4cos(¯a,¯b)=20

cos(¯a,¯b)=12
π(¯a,¯b)=π3
(¯a,¯b)=(ππ3)=2π3

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