JEE Mains · Maths · STD 12 - 10. vector algebra
Let \( \vec a ,\vec b\) and \(\vec c \) be three non-zero vectors such that no two of them are collinear and \(\left( {\vec a \times \vec b} \right) \times \vec c = \frac{1}{3}\left| \vec b \right|\left| \vec c \right|\vec a\). If \(\theta \) is the angle between vectors \(\vec b\) and \(\vec c\) , then a value of \(\sin \theta \) is :
- A \(\frac{{ - 2\sqrt 3 }}{3}\)
- B \(\;\frac{{2\sqrt 2 }}{3}\)
- C \(\;\frac{{ - \sqrt 2 }}{3}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(\;\frac{{2\sqrt 2 }}{3}\)
Step-by-step Solution
Detailed explanation
\(\left( {\vec a \times \vec b} \right) \times \vec c = \left( {\frac{1}{3}} \right)\left| {\vec b} \right|\left| {\vec c} \right|\vec a\)…
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