The resultant of two vectors is maximized when the two vectors are in the same direction.
If we have two vectors \(\mathbf{A}\) and \(\mathbf{B}\), the magnitude of their resultant \(\mathbf{R}\) can be calculated as:
\[ R = |\mathbf{A}| + |\mathbf{B}| \]
where \(|\mathbf{A}|\) is the magnitude of vector \(\mathbf{A}\) and \(|\mathbf{B}|\) is the magnitude of vector \(\mathbf{B}\).
If the vectors are not in the same direction, the resultant can be calculated using the law of cosines:
\[ R = \sqrt{|\mathbf{A}|^2 + |\mathbf{B}|^2 + 2|\mathbf{A}||\mathbf{B}|\cos(\theta)} \]
where \(\theta\) is the angle between the two vectors.
To maximize the resultant, \(\cos(\theta)\) should be maximized, which occurs when \(\theta = 0^\circ\) (the vectors are in the same direction). Thus, the maximum resultant occurs when the vectors are aligned (i.e., both pointing in the same direction).