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Question

A parallelogram is constructed on the vectors a=3αβ,b=α+3β, if |α|=|β|=2 and angle between α and β is π3, then length of a diagonal of the parallelogram is

A
45
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B
43
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C
417
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D
None of these
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Solution

The correct option is D None of these
a and b are two adjacent sides of ll gm so sum of sides (adjacent)
will give length of diagonal.
a=3αβ of α+3β
a+b=4α+2β
|a+b|=(4α)2+(2β)2+2(4α)(2β)
=16|α|2+4|β|2+16αβ
=16(4)+4(4)+16|α||β|cosθ
where θ is angle between α&β
|a+b|=64+16+64cosπ3=64+16+32=112=47
so required length of diagonal is 47.
Answer : option (D)

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