Question

can the sum of the magnitudes of two vectors ever be equal to the magnitude of the sum of the same two vectors? if no, why not? if yes, when? , ayuda por favor

Answer 1

1. The magnitude of the sum of two vectors is maximum when they are parallel (= sum of their magnitudes) and is minimal when they are antiparallel (= difference of their magnitudes); therefore the answer is yes.

2. Returning to the idea above, if they are antiparallel, the magnitude of the difference = sum of their magnitudes, therefore, is greater than the magnitude of one of them.

Obviously, in that case the magnitude of its sum would be = the difference of its magnitudes, which is less than the magnitude of the difference. Again the answer to both questions is yes.

If you want to make a graphic demonstration, you just have to draw a couple of vectors with the common origin and use the parallelogram method.