JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\hat{a}, \hat{b}\) be unit vectors. If \(\vec{c}\) be a vector such that the angle between \(\hat{ a }\) and \(\overrightarrow{ c }\) is \(\frac{\pi}{12}\), and \(\hat{ b }=\overrightarrow{ c }+2(\overrightarrow{ c } \times \hat{ a })\), then \(|6 \overrightarrow{ c }|^{2}\) is equal to
- A \(6(3-\sqrt{3})\)
- B \(3+\sqrt{3}\)
- C \(6(3+\sqrt{3})\)
- D \(6(\sqrt{3}+1)\)
Answer & Solution
Correct Answer
(C) \(6(3+\sqrt{3})\)
Step-by-step Solution
Detailed explanation
\(|\hat{b}|^{2}=|\vec{c}+2(\vec{c} \times \hat{a})|^{2}\) \(|\hat{ b }|^{2}=| c |^{2}+4|\overrightarrow{ c } \times \hat{ a }|^{2}+4 \overrightarrow{ c } \cdot(\overrightarrow{ c } \times \hat{ a })\) \(1=|c|^{2}+4|c|^{2} \sin ^{2} \frac{\pi}{12}+0\)…
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