TS EAMCET · Maths · Vector Algebra
If \(\mathbf{a}, \mathbf{b}\) and \(\overline{\mathbf{c}}\) are three vectors with magnitudes 1,1 and 2 respectively and \(\mathbf{a} \times(\mathbf{a} \times \mathbf{c})+\mathbf{b}=0\), then the angle between \(a\) and \(c\) is
- A \(\frac{2 \pi}{5}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }|\mathbf{a}|=1|\mathbf{b}|=1 \quad|\mathbf{c}|=2 \\ & \mathbf{a} \times(\mathbf{a} \times \mathbf{c})+\mathbf{b}=0 \\ & \Rightarrow \quad \mathbf{a} \times(\mathbf{a} \times \mathbf{c})=-\mathbf{b} \\ & \Rightarrow \quad[\mathbf{a} \times(\mathbf{a}…
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