Problem 82.

Can two displacements (vectors) of different magnitudes be combined to give a zero displacement (resultant)?

Solution:

The sum of two vectors (displacements) is zero only if

1. vectors have opposite directions;

2. vectors have the same magnitude.

Indeed, the sum of two vectors is shown in the figure below for a fixed orientation of the first vector and different orientations of the second vector. In the picture we assume that the magnitude of the second vector is less than the magnitude of the first vector.

We can see that the sum of two vectors has the smallest magnitude when the vectors have opposite directions. In this case the sum is zero only if the vectors have the same magnitude.