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1)

Let ˜a,˜b and  ˜c be three unit vectors such that  ˜a×(˜bטc)=32(˜b+˜c) . If  ˜b is not parallel to ˜c , then the angle between ˜a and ˜b is


A) 3π4

B) π2

C) 2π3

D) 5π6

Answer:

Option D

Explanation:

Given  ˜a∣=∣˜b∣=∣˜c∣=1

 and   ˜a×(˜bטc)=32(˜b+˜c)

Now consider ˜a×(˜bטc)=32(˜b+˜c)

(˜a.˜c)˜b(˜a.˜b)˜c=32˜b+32˜c

On comparing , we get

                   ˜a.˜b=32

⇒∣˜a∣∣˜bcosθ=32

cosθ=32[∵∣˜a∣=∣˜b∣=1]

cosθ=cos(ππ6)

θ=5π6