Can the sum of two equal vectors be equal to either of vectors?

Answer 1

We have to be very careful with this one:

If two vectors with equal magnitudes point in directions that are 120° apart,

then their sum has the same magnitude that each of them has.

But vectors are not "equal" unless they have the same magnitude and the

same direction. If the two originals in the question are truly equal, then they

must point in the same direction, their sum can only be double the same

magnitude and in the same direction, and it's obviously not equal to the

original two vectors. So the strict answer to the question is a simple "no".

If they're separated by 120°, then they're not really equal. Their sum has the

same magnitude that each of them has, but it can't be 'equal' to either of the

original ones, because it doesn't point in the same direction that either of them

does.

This whole discussion is like "walking on eggs".

We note further that the question is a bit confused too. First it says that two

vectors are equal, then it asks whether another vector is equal to "either" one.

If the original two are truly equal, then anything that's equal to one of them

must be equal to both of them.

If you're still following this, then I offer you my congratulations.

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Trivially, the sum of two null vectors is also a null vector. And that is the only possible instance when the question can be properly answered in the positive.