Q.

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

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a

45

b

43

c

47

d

None of these

answer is B.

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Detailed Solution

AC→=a→+b→∴     |AC→|=|a→+b→|∴ |AC→|2=|a→|2+|b→|2+2a→⋅b→=|3α→−β→|2+|α→+3β→|2+2(3α→−β→)⋅(α→+3β→)=16|α→|2+4|β→|2+16α→⋅β→=80+16(2)(2)(1/2)=112∴ |AC→|=47|BD→|=|a→−b→|
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