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 DExplanation: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∣∣˜b∣cosθ=−√32 ⇒cosθ=−√32[∵∣˜a∣=∣˜b∣=1] ⇒cosθ=cos(π−π6) ⇒θ=5π6