Can resultant magnitude of two vectors be smaller than the magnitude of either vector?

yes

certainly if 180º apart

To determine if the resultant magnitude of two vectors can be smaller than the magnitude of either vector, we need to understand vector addition. When two vectors are added, the resultant is obtained by adding the corresponding components of the vectors.

In general, the magnitude of the resultant vector can be larger, smaller, or equal to the magnitudes of the individual vectors, depending on the angle between them.

If the two vectors are in the same direction (angle < 90 degrees), the magnitude of the resultant vector will be larger than the magnitude of either vector. This is because their magnitudes add up.

If the two vectors are in opposite directions (angle = 180 degrees), the magnitude of the resultant vector will be equal to the difference of their magnitudes. In this case, it is not possible for the magnitude of the resultant to be smaller than either vector.

However, if the two vectors are at an angle between 0 and 180 degrees, the magnitude of the resultant vector can be smaller than either vector. This happens when the angle between the two vectors is obtuse (greater than 90 degrees) and the magnitudes subtract from each other.

To find the resultant vector in such cases, you can use vector addition equations or graphical methods like the parallelogram or triangle rule. By adding the vectors' components or using the graphical method, you can determine the resultant vector and compare its magnitude with the magnitudes of the individual vectors.