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प्रश्न
If the vectors \[\vec{a}\] and \[\vec{b}\] are such that \[\left| \vec{a} \right| = 3, \left| \vec{b} \right| = \frac{2}{3}\] and \[\vec{a} \times \vec{b}\] is a unit vector, then write the angle between \[\vec{a}\] and \[\vec{b}\]
उत्तर
Let the angle between \[\vec{a}\] and \[\vec{b}\] be \[\theta\] It is given that \[\vec{a} \times \vec{b}\] is a unit vector.
\[\therefore \left| \vec{a} \times \vec{b} \right| = 1\]
\[ \Rightarrow \left| \vec{a} \right|\left| \vec{b} \right|\sin\theta = 1\]
\[ \Rightarrow 3 \times \frac{2}{3} \times \sin\theta = 1\]
\[ \Rightarrow \sin\theta = \frac{1}{2}\]
\[ \Rightarrow \theta = \frac{\pi}{6}\]
Thus, the angle between \[\vec{a}\] and \[\vec{b}\] is \[\frac{\pi}{6}\]
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