Determine whether the vectors \( \mathbf{A} = [1, 2, 3] \) and \( \mathbf{B} = [4, -2, 0] \) are orthogonal.

Step 1 ：Calculate the dot product of vectors \( \mathbf{A} \) and \( \mathbf{B} \). The dot product is defined as \( \mathbf{A} \cdot \mathbf{B} = \sum_{i=1}^{n} a_i b_i \), where \( a_i \) and \( b_i \) are the components of \( \mathbf{A} \) and \( \mathbf{B} \) respectively.

Step 2 ：Substitute the given values into the dot product formula: \( \mathbf{A} \cdot \mathbf{B} = (1)(4) + (2)(-2) + (3)(0) = 4 - 4 + 0 \).

Step 3 ：If the dot product of two vectors is 0, they are orthogonal. So, we check the result of our calculation.