Let \(\vec{a} = 3\hat{i} - 4\hat{j} + 2\hat{k}\) and \(\vec{b} = -\hat{i} + 2\hat{j} - 3\hat{k}\). Find \(\vec{a} - \vec{b}\).

Step 1 ：Step 1: Write down the vectors \(\vec{a}\) and \(\vec{b}\): \(\vec{a} = 3\hat{i} - 4\hat{j} + 2\hat{k}\) and \(\vec{b} = -\hat{i} + 2\hat{j} - 3\hat{k}\)

Step 2 ：Step 2: Subtract \(\vec{b}\) from \(\vec{a}\) by subtracting the corresponding components of \(\vec{b}\) from \(\vec{a}\): \(\vec{a} - \vec{b} = (3 - (-1))\hat{i} + (-4 - 2)\hat{j} + (2 - (-3))\hat{k} = 4\hat{i} - 6\hat{j} + 5\hat{k}\)