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Question

If ¯¯¯u=¯¯¯a+¯¯b, ¯¯¯v=¯¯¯a¯¯b, |a|=|¯¯b|=2, then |¯¯¯uׯ¯¯v|=

A
16(¯¯¯a¯¯b)2
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B
216(¯¯¯a¯¯b)2
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C
316(¯¯¯a¯¯b)2
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D
0
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Solution

The correct option is D 216(¯¯¯a¯¯b)2
U×V=(a+b)×(ab)
=a×b+b×a
=2b×a
U×V=2b×a(a×b2+(ab)2=ab)
=2|a|2b2(ab)2
=216(ab)2

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