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Q.

If a→ and b→ are non-zero vectors such that |a→+b→|=|a→−2b→| then

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a

2a→⋅b→=|b→|2

b

a→⋅b→=|b→|2

c

Least value of |a→⋅b |→+1|b→|2+2 is 2

d

least value of |a→⋅b→|+1|b→|2+2 is 2-1

answer is A.

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Detailed Solution

|a→+b→|=|a→−2b→| ⇒a→+b→2=|a→−2b→|2⇒a     →⋅b→=|b→|22also  a→⋅b→+1|b→|2+2=|b→|2+22+1|b→|2+2−1(using A.M. ≥G.M.)≥2−1
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