If $\vec{a} = \hat{i} + 2\hat{j} - \hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} + 2\hat{k}$, what is $2\vec{a} - \vec{b}$?

Explanation

1. 01

   $2\vec{a} = 2\hat{i} + 4\hat{j} - 2\hat{k}$.

2. 02

   Subtract component by component: $-\hat{i} + 5\hat{j} - 4\hat{k}$.