Is it possible to combine two vectors of different magnitudes to give a zero resultant? If not, can three vectors be so combined?

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lfryerda eNotes educator| Certified Educator

With vectors, it is not possible to combine two of different magnitudes (through addition or subtraction, your question did not say) to get a zero result since the vectors need to cancel out the resultant's magnitude.  Since vectors add through the triangle law (and subtraction is the same, just with vectors in the opposite direction), then there is no way to construct a vector that has zero resultant with different magnitudes for the other two sides.

However, with three vectors, there are many ways to get a zero resultant, where the vectors have different magnitudes.  Construct any scalene triangle, and number the vertices.  Then let each vector go from one vertex to the next.  The sum of the three vectors is the zero resultant, since the end point is the same as the starting point.

It is not possible with two vectors, and possible with three vectors.