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Question
Find the angle between two vectors \[\vec{a} \text{ and } \vec{b}\] with magnitudes 1 and 2 respectively and when \[\left| \vec{a} \times \vec{b} \right| = \sqrt{3} .\]
Solution
\[\text{ Let } \theta \text{ be the angle between } \vec{a} \text{ and } \vec{b} . \]
\[\text{ We know } \]
\[\left| \vec{a} \times \vec{b} \right| = \left| \vec{a} \right| \left| \vec{b} \right| \sin \theta\]
\[ \Rightarrow \sqrt{3} = \left( 1 \right) \left( 2 \right) \sin \theta\]
\[ \Rightarrow \sin \theta = \frac{\sqrt{3}}{2}\]
\[ \Rightarrow \theta = \frac{\pi}{3}\]
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