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Q.

If  a→ and b→ are two unit vectors inclined at an angle π3 then  {a→×(b→+a→×b→)}⋅b→ is equal to

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a

-34

b

14

c

34

d

12

answer is A.

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Detailed Solution

{a→×(b→+a→×b→)}⋅b→={a→×b→+a→×(a→×b→)}⋅b→=[a→b→b→]+{(a→⋅b→)a→−(a→⋅a→)b→}⋅b→=0+(a→⋅b→)2−(a→⋅a→)(b→⋅b→)=cos2⁡π3−1=−34
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