JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\overrightarrow{ a }\) and \(\overrightarrow{ b }\) are unit vectors, then the greatest value of \(\sqrt{3}|\overrightarrow{ a }+\overrightarrow{ b }|+|\overrightarrow{ a }-\overrightarrow{ b }|\) is
- A \(6\)
- B \(5\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(\sqrt{3}|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|\) \(=\sqrt{3}(\sqrt{2+2 \cos \theta})+\sqrt{2-2 \cos \theta}\) \(=\sqrt{6}(\sqrt{1+\cos \theta})+\sqrt{2}(\sqrt{1-\cos \theta})\) \(=2 \sqrt{3}\left|\cos \frac{\theta}{2}\right|+2\left|\sin \frac{\theta}{2}\right|\)…
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