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AP EAMCET · Maths · Vector Algebra

If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are non-zero vectors such that \((\mathbf{a} \times \mathbf{b}) \times \mathbf{c}\) \(=\frac{1}{3}|\mathbf{b}||\mathbf{c}| \mathbf{a}, \mathbf{c} \perp \mathbf{a}\) and \(\theta\) is the angle between the vectors \(\mathbf{b}\) and \(\mathbf{c}\), then \(\sin \theta\) is equal to

  1. A \(\frac{2 \sqrt{2}}{3}\)
  2. B \(\frac{1}{3}\)
  3. C \(\frac{\sqrt{2}}{3}\)
  4. D \(\frac{2}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{2 \sqrt{2}}{3}\)

Step-by-step Solution

Detailed explanation

Here, \(a, b\) and \(c\) are non-zero vectors \(\mathrm{C} \perp \mathrm{a} \Rightarrow c . a=\) 0 and \(\theta\) is the angle between the vectors \(b\) and \(c\).…