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Q.

Let a¯,b¯,c¯ be three vectors such that |a→|=1,|b¯|=1 and |c¯|=2 and if a¯×(a¯×c¯)+b¯=0¯ , then  angle between a¯ and c¯ can be

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a

π3

b

π4

c

π6

d

π2

answer is C.

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Detailed Solution

a¯×(a¯×c¯)+b¯=0¯(a¯⋅c¯)a¯−(a¯⋅a¯)c¯+b¯=0¯(a¯⋅c¯)a¯−c¯=−b¯Ka¯−c¯=−b¯, where K=a.bK2a¯2+c¯2−2K2=b¯2K=±3⇒cos⁡θ=±32
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