TS EAMCET · Maths · Vector Algebra
Let \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be three unit vectors such that \(\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{1}{\sqrt{2}}(\mathbf{b}+\mathbf{c})\) and \(\mathbf{b}\) is not parallel to c. If \(\alpha\) and \(\beta\) are the angles between \(\mathbf{a}, \mathbf{b}\) and a,c respectively then \(\alpha-\beta=\)
- A \(\frac{3 \pi}{4}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{2}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Given \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) be three unit vectors \(\therefore \quad|\mathbf{a}|=|\mathbf{b}|=|\mathbf{c}|=1\) Now, \(\quad \mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{1}{\sqrt{2}}(\mathbf{b}+\mathbf{c})\)…
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