$\lvert \vec{a} \rvert = 2$, $\lvert \vec{b} \rvert = 3$, and the angle between them is $60^\circ$. What is $\lvert \vec{a} - \vec{b} \rvert$?

Explanation

1. 01

   $\vec{a} \cdot \vec{b} = 2 \times 3 \times \cos 60^\circ = 3$.

2. 02

   $\lvert \vec{a} - \vec{b} \rvert^{2} = 4 + 9 - 2(3) = 7$, so $\sqrt{7}$.