$\lvert \vec{a} \rvert = 3$, $\lvert \vec{b} \rvert = 4$, and the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{6}$. What is $\lvert \vec{a} \times \vec{b} \rvert$?

Explanation

1. 01

   $\lvert \vec{a} \times \vec{b} \rvert = \lvert \vec{a} \rvert \lvert \vec{b} \rvert \sin \theta = 3 \times 4 \times \sin\frac{\pi}{6}$.

2. 02

   $\sin\frac{\pi}{6} = \frac{1}{2}$, so $\lvert \vec{a} \times \vec{b} \rvert = 6$.