If \(|\vec{a}| = 4\), \(|\vec{b}| = 3\), \(|\vec{a}\times\vec{b}| = 6\) and the angle between \(\vec{a}\) and \(\vec{b}\) is acute, then the angle between \(\vec{a}\) and \(\vec{b}\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{\pi}{6}\)
The magnitude of the vector product is \(|\vec{a}\times\vec{b}| = |\vec{a}|\,|\vec{b}|\sin\theta\). So
\(6 = 4\times 3\times\sin\theta\)
\( \displaystyle \sin\theta = \frac{6}{12} = \frac{1}{2} \)
Both \(\frac{\pi}{6}\) and \(\frac{5\pi}{6}\) have this sine; the angle is acute, so
\( \displaystyle \theta = \frac{\pi}{6} \)