No, they could be equal
If the two vectors are opposites (180 degrees apart) like r and -r, then the sum of their magnitudes is the magnitude of their sum.
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North 1 plus East 1 gives NorthEast 1.414.
North 1 plus South 1 gives 0.
North 1 plus North 1 gives North 2, which is equal to, not less than 1+1.
Of course. The resultant of +4 north and +4 south is zero.
When adding you expect an answer that is greater than either number.
Answer2: Yes. If the two vectors have opposite directions their sum could be zero and smaller than either.
If the two vectors point in the same direction, the sum of the magnitudes will be equal to the magnitude of the sum of the vectors.
That's exactly the situation when both vectors have the same direction. Then
the magnitude of their sum is equal to the sum of their individual magnitudes.
(1,1) + (-1,4) = (0,5)
only if the vectors have the same direction
Their magnitudes are exactly equal and their directions are exactly opposite.
When two vectors with different magnitudes and opposite directions are added :-- The magnitude of the sum is the difference in the magnitudes of the two vectors.-- The direction of the sum is the direction of the larger of the two vectors.
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.
-- A singe vector with a magnitude of zero produces a zero resultant.-- Two vectors with equal magnitudes and opposite directions produce a zero resultant.
only if the vectors have the same direction
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.
Two is the minimum number of vectors that will sum to zero.
180 degrees. Then the sum of the two vectors has a magnitude equal to the difference of their individual magnitudes.
Sure, if the two vectors point in the same direction.When we need the sum of magnitudes of two vectors we simply add the magnitudes, but to get the magnitude of the sum of these two vectors we need to add the vectors geometrically.Formula to find magnitude of the sum of these two vectors is sqrt[ |A|2 +|B|2 +2*|A|*|B|*cos(z) ] where |A| and |B| are magnitudes of two A and B vectors, and z is the angle between the two vectors.Clearly, magnitude of sum of two vectors is less than sum of magnitudes(|A| + |B|) for all cases except when cos(z)=1(for which it becomes = |A| + |B| ). Cos(z)=1 when z=0, i.e. the vectors are in the same direction(angle between them is 0).Also if we consider addition of two null vectors then their sum is zero in both ways of addition.So, we get two caseswhen the two vectors are in same direction, andwhen the two vectors are null vectors.In all other cases sum of magnitudes is greater than magnitude of the sum of two vectors.
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.
If 'A' and 'B' are vectors, and their magnitudes are equal, andtheir directions are opposite, then their vector sum is zero.
No. The largest possible resultant magnitude is the sum of the individual magnitudes.The smallest possible resultant magnitude is the difference of the individual magnitudes.
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
Their magnitudes are exactly equal, and their directions are exactly opposite.
Their magnitudes are exactly equal and their directions are exactly opposite.