Q: When are two vectors equal and when are identical?

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If two vectors are represented by the same magnitude and direction they are said to be equal.

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.

With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.

Yes, if one of the vectors is the null 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.

Related questions

Two vectors are identical when all their components are identical. An alternative definition, for vectors used in physics, is that they are identical when both the magnitude and the direction are identical.

No, the resultant of two equal vectors will have a magnitude that is not equal to the magnitude of the original vectors. When two vectors are added together, the resulting vector will have a magnitude that depends on the angle between the two vectors.

If two vectors are represented by the same magnitude and direction they are said to be equal.

Yes.

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.

With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.

Equal vectors are vectors having same direction of action or orientation as well as same magnitude. If two or more vectors have same magnitude but different direction then they cannot be called equal vectors. This shows that direction is important for equal vectors.

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.

Yes. A vector has magnitude and direction. If the vectors have equal magnitude and directly opposite directions their sum will be zero.

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.

Yes, if one of the vectors is the null 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.