AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three unit vectors such that \(\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{\sqrt{3}}{2} \mathbf{b}+\frac{1}{2} \mathbf{c}\), then the angles between \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{a}, \mathbf{c}\) respectively are
- A \(60^{\circ}, 30^{\circ}\)
- B \(120^{\circ}, 30^{\circ}\)
- C \(60^{\circ}, 150^{\circ}\)
- D \(120^{\circ}, 150^{\circ}\)
Answer & Solution
Correct Answer
(B) \(120^{\circ}, 30^{\circ}\)
Step-by-step Solution
Detailed explanation
Given that \(\mathbf{a} \times \mathbf{( b} \times \mathbf{c})=\frac{\sqrt{3}}{2} \mathbf{b}+\frac{1}{2} \mathbf{c}\) \(\Rightarrow \quad \text { (a . c) } \mathbf{b}-\mathbf{( a} \cdot \mathbf{b}) \mathbf{c}=\frac{\sqrt{3}}{2} \mathbf{b}+\frac{1}{2} \mathbf{c}\) Let angle…
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