Wiki User
∙ 12y agoWe 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 is also a null vector. And that is the only possible instance when the question can be properly answered in the positive.
Wiki User
∙ 12y agoYes, 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 one of them has a magnitude of zero, so, effectively, no.
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.
Yes, if one of the vectors is the null vector.
No, the sum of two vectors cannot be equal to either of the vectors. Adding two vectors results in a new vector, with a magnitude and direction that is determined by the individual vectors being added.
Only if one of them has a magnitude of zero, so, effectively, no.
No, the statement is incorrect. The sum of two vectors of equal magnitude will not equal the magnitude of either vector. The sum of two vectors of equal magnitude will result in a new vector that is larger than the original vectors due to vector addition. The magnitude of the difference between the two vectors will be smaller than the magnitude of either vector.
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 one of them has a magnitude of zero, so, effectively, no.
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.
When the vectors are parallel, i.e. both have the same direction.
Yes, the Triangle Inequality states that the sum of the magnitudes of two vectors can never be equal to the magnitude of the sum of those two vectors. Mathematically, if vectors a and b are non-zero vectors, then |a| + |b| ≠ |a + b|.
Yes.
The magnitudes of two vectors are added when the vectors are parallel to each other. In this case, the magnitude of the sum is equal to the sum of the magnitudes of the two vectors.
When the angle between any two component vectors is either zero or 180 degrees.