Final answer:
The magnitude of the sum of two vectors \(M\) and \(J\), denoted as \(|M + J|\), will not be equal to the magnitude of either vector if the vectors are orthogonal, have different magnitudes or directions, or are antiparallel. It will only be equal if the vectors have the same magnitude and direction.
Step-by-step explanation:
The magnitude of the sum of two vectors \(M\) and \(J\), denoted as \(|M + J|\), is not necessarily equal to the magnitude of either individual vector. The magnitudes will not be equal if the vectors are orthogonal (at a 90-degree angle to each other), because in this case, the magnitude of their sum is a result of the Pythagorean theorem and will be different from the magnitudes of either \(M\) or \(J\).
If the two vectors have different magnitudes or directions, the magnitude of their sum will also be not equal to the magnitudes of the original vectors. Additionally, if the vectors are antiparallel (parallel but in opposite directions), their magnitudes will not cancel each other because they will add algebraically based on vector addition rules, resulting in a sum whose magnitude depends on the difference in magnitudes of \(M\) and \(J\).
Only when the vectors have exactly the same magnitude and direction would their sum have a magnitude equal to the individual vectors, which is a unique scenario.