$\lvert \vec{a} \rvert = 2$, $\lvert \vec{b} \rvert = 5$ and $\vec{a} \cdot \vec{b} = 6$. What is $\lvert \vec{a} \times \vec{b} \rvert$?

Explanation

1. 01

   $\lvert \vec{a} \times \vec{b} \rvert^{2} + (\vec{a} \cdot \vec{b})^{2} = \lvert \vec{a} \rvert^{2}\lvert \vec{b} \rvert^{2}$, since $\sin^{2} \theta + \cos^{2} \theta = 1$.

2. 02

   $\lvert \vec{a} \times \vec{b} \rvert^{2} = 100 - 36 = 64$, so $\lvert \vec{a} \times \vec{b} \rvert = 8$.