Question

when will the resultant of the two vectors be at the maxium

Answer 1

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).