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When is the sum of the magnitudes of two vectors equal to the magnitude of the sum of the vectors?
Wiki User
∙ 14y ago
When the vectors are parallel, i.e. both have the same direction.
Wiki User
∙ 14y ago
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Can the sum of the magnitudes of two vectors ever b equal to the the sum of these two vectors?
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 angle between two vectors is equal to zero?
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.
How can the resultant of two vecters of the same magnitude be equal to the magnitude of either vector?
If the directions of two vectors with equal magnitudes differ by 120 degrees, then the magnitude of their sum is equal to the magnitude of either vector.
Can the sum of two vectors of unequal magnitudes be a zero vector?
The sum of two unequal vectors can not be zero, because we can get minimum magnitude of two vectors when they are in opposite direction and can only get zero magnitude when they are equal in magnitude.................................... Answered by: SAJJAD AHMED(bfps doha Qatar)
Suppose you have two vectors that have different magnitudes can the vectors sum ever be 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.
Can the sum of the magnitudes of two vectors ever b equal to the the sum of these two vectors?
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.
The sum of two vectors is a minimum when the angle between them is what?
180 degrees. Then the sum of the two vectors has a magnitude equal to the difference of their individual magnitudes.
Can the sum of the magnitudes of two vectors ever be equal to the magnitudes of the sum of these two vectors?
only if the vectors have the same direction
When the angle between two vectors is equal to zero?
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.
Can the sum of magnitudes of two vectors ever be equal to the magnitude of the sum of these two vectors?
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.
How can the resultant of two vecters of the same magnitude be equal to the magnitude of either vector?
If the directions of two vectors with equal magnitudes differ by 120 degrees, then the magnitude of their sum is equal to the magnitude of either vector.
Can the sum of two vectors of unequal magnitudes be a zero vector?
The sum of two unequal vectors can not be zero, because we can get minimum magnitude of two vectors when they are in opposite direction and can only get zero magnitude when they are equal in magnitude.................................... Answered by: SAJJAD AHMED(bfps doha Qatar)
Suppose you have two vectors that have different magnitudes can the vectors sum ever be 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.
Can the sum of of the magnitudes of two vectors ever be equal to the magnitudes of the sum of these two vectors?
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. ?? 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.
What is the minimum possible magnitude of 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.
Adding vectors that act in the opposite direction?
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.
Can the magnitude of the resultant of two vector be greater than the sum of magnitudes of individual vectors?
No.
