Given two vectors \(\vec{a} = 3\hat{i} - 2\hat{j} + \hat{k}\) and \(\vec{b} = -\hat{i} + 2\hat{j} - 3\hat{k}\), find the vector \(\vec{a} - \vec{b}\).

Step 1 ：First, we subtract the components of vector \(\vec{b}\) from the components of vector \(\vec{a}\)

Step 2 ：The \(i\) component of \(\vec{a} - \vec{b}\) is \(3 - (-1) = 4\)

Step 3 ：The \(j\) component of \(\vec{a} - \vec{b}\) is \(-2 - 2 = -4\)

Step 4 ：The \(k\) component of \(\vec{a} - \vec{b}\) is \(1 - (-3) = 4\)