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.
* * * * *
Trivially, the sum of two null vectors (vectors with zero magnitude) is also a null vector.
And that is the only possible instance when the question can be properly answered with a 'yes'.
Nope! I can think of another way . . . If one of the vectors is a null, then their sum
is equal to the other vector.
Yes, if one of the vectors is the null vector.
Only if one of them has a magnitude of zero, so, effectively, no.
Not really. The sum of the magnitudes is a scalar, not a vector - so they can't be equal. But the sum of the two vectors can have the same magnitude, if both vectors point in the same direction.
When the vectors are parallel, i.e. both have the same direction.
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
Yes, if one of the vectors is the null vector.
Only if one of them has a magnitude of zero, so, effectively, no.
Not really. The sum of the magnitudes is a scalar, not a vector - so they can't be equal. But the sum of the two vectors can have the same magnitude, if both vectors point in the same direction.
only if the vectors have the same direction
When the vectors are parallel, i.e. both have the same direction.
Only if one of them has a magnitude of zero, so, effectively, no.
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
Only if one of them has a magnitude of zero, so, effectively, no.
The minimum possible magnitude that results from the combintion of two vectors is zero. That's what happens when the two vectors have equal magnitudes and opposite directions.The maximum possible magnitude that results from the combintion of two vectors is the sum of the two individual magnitudes. That's what happens when the two vectors have the same direction.
Assuming you mean sum and not some, the answer is No.
Two is the minimum number of vectors that will sum to zero.