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 Given a parallelogram ABCD . If |AB=a,|AD∣=b and |AC|=c, then DBAB  has the value : 

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a
3a2 + b2 −c22
b
a2 +3 b2 −c22
c
a2 − b2 +  3c22
d
none of these

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detailed solution

Correct option is A

To find (a→−b→)⋅a→, i.e. |a→|2−a→⋅b→     ………..(1)  Now a→+b→=c→⇒ |a→|2+|b→|2+2a→⋅b→=|c→|2⇒2a→⋅b→=|c→|2-|a→|2-|b→|2 a→⋅b→=|c→|2-|a→|2-|b→|22 Substitute the value of a→⋅b→ in eqn. (1)a2→-|c→|2-|a→|2-|b→|223a→2+b→2-c→22


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