Given vector \(\mathbf{a} = [3, 2, 1]\) and vector \(\mathbf{b} = [1, 4, 2]\), find the sum of these two vectors \(\mathbf{a} + \mathbf{b}\).

Step 1 ：The addition of two vectors is performed component-wise. So, we add the corresponding components of vectors \(\mathbf{a}\) and \(\mathbf{b}\) to get the vector \(\mathbf{a} + \mathbf{b}\).

Step 2 ：The first component of \(\mathbf{a} + \mathbf{b}\) is \(3 + 1 = 4\).

Step 3 ：The second component of \(\mathbf{a} + \mathbf{b}\) is \(2 + 4 = 6\).

Step 4 ：The third component of \(\mathbf{a} + \mathbf{b}\) is \(1 + 2 = 3\).

Step 5 ：Therefore, the vector \(\mathbf{a} + \mathbf{b}\) is \([4, 6, 3]\).