Question:
If \(\left|\vec{a}\right| = 2\), \(\left|\vec{b}\right| = 3\) and \(\left|2\vec{a} - \vec{b}\right| = 5\), then \(\left|2\vec{a} + \vec{b}\right|\) equals :
If \(\left|\vec{a}\right| = 2\), \(\left|\vec{b}\right| = 3\) and \(\left|2\vec{a} - \vec{b}\right| = 5\), then \(\left|2\vec{a} + \vec{b}\right|\) equals :
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Square the given magnitude to get \(\vec a\cdot\vec b = 0\), then evaluate \(|2\vec a + \vec b|^2\).
Updated On: Nov 11, 2026
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The Correct Option is A
Solution and Explanation
\(|2\vec a - \vec b|^2 = 4|\vec a|^2 + |\vec b|^2 - 4\,\vec a\cdot\vec b = 16 + 9 - 4\,\vec a\cdot\vec b = 25\), so \(\vec a\cdot\vec b = 0\).
Then \(|2\vec a + \vec b|^2 = 16 + 9 + 4\,\vec a\cdot\vec b = 25\).
Hence \(|2\vec a + \vec b| = 5\).
Answer: (1) 5
Then \(|2\vec a + \vec b|^2 = 16 + 9 + 4\,\vec a\cdot\vec b = 25\).
Hence \(|2\vec a + \vec b| = 5\).
Answer: (1) 5
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