Question:
If \(\hat a,\ \hat b\) and \(\hat c\) are unit vectors satisfying \(\hat a-\sqrt3\,\hat b+\hat c=\vec 0\), then the angle between the vectors \(\hat a\) and \(\hat c\) is :
If \(\hat a,\ \hat b\) and \(\hat c\) are unit vectors satisfying \(\hat a-\sqrt3\,\hat b+\hat c=\vec 0\), then the angle between the vectors \(\hat a\) and \(\hat c\) is :
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Write \(\hat a+\hat c=\sqrt3\,\hat b\) and take the squared magnitude of both sides.
Updated On: Oct 31, 2026
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{3}\)
- \(\frac{\pi}{6}\)
- \(\frac{\pi}{2}\)
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The Correct Option is B
Solution and Explanation
\(\hat a+\hat c=\sqrt3\,\hat b\). Square the magnitudes: \(|\hat a|^2+|\hat c|^2+2\,\hat a\cdot\hat c=3|\hat b|^2\).
\(1+1+2\cos\theta=3\Rightarrow\cos\theta=\frac12\Rightarrow\theta=\frac{\pi}{3}\).
Answer: (2) \(\frac{\pi}{3}\)
\(1+1+2\cos\theta=3\Rightarrow\cos\theta=\frac12\Rightarrow\theta=\frac{\pi}{3}\).
Answer: (2) \(\frac{\pi}{3}\)
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