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What is the Minimum number of vectors with unequal magnitudes whose vector sum can be zero?
Wiki User
∙ 11y ago
-- A singe vector with a magnitude of zero produces a zero resultant.
-- Two vectors with equal magnitudes and opposite directions produce a zero resultant.
Wiki User
∙ 12y ago
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What is the smallest number of vectors that can be added to give a zero resultant?
Two.Equal magnitudes in opposite directions.
What are different conditions that could make vector product zero?
First of all, you have to define what you mean by "vector product".-- The "dot product" is zero if the vectors are perpendicular, regardless of their magnitudes.-- The "cross product" is zero if the vectors are collinear or opposite, regardless of their magnitudes.-- Perhaps when you say "product", you mean the "result" of two vectors, whicha mathematician or physicist would cal their "sum".The sum of two vectors is zero if their magnitudes are equal and their directionsdiffer by 180 degrees.An infinite number of other possibilities exist for a sum of zero, depending on themagnitudes and directions of two vectors.
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.
Is it possible to combine 2 equal vectors to give a zero resultant?
With equal angles between them - which in this case results in 360° / 3 = 120° separation between the angles.
How do vectors add?
Just add their magnitudes. The combined vector will have the same direction as the original vectors.Just add their magnitudes. The combined vector will have the same direction as the original vectors.Just add their magnitudes. The combined vector will have the same direction as the original vectors.Just add their magnitudes. The combined vector will have the same direction as the original vectors.
What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?
Two is the minimum number of vectors that will sum to zero.
What is the smallest number of vectors that can be added to give a zero resultant?
Two.Equal magnitudes in opposite directions.
Can 3 unequal vectors add up to give the zero vector?
Yes, they certainly can.Simplest example:(10 pounds north) + (4 pounds south) + (6 pounds south) = Zero.But any number of non-zero vectors, more than one, can add up to zeroif they have the right magnitudes and directions.
What is the minimum number of vectors in different planes that can be added to give a zero resultant?
There is no minimum.
What must be the minimum number of vectors in a space is required so that their sum is zero?
If none of the individual vectors has a magnitude of zero, thenthe minimum number that can combined to make zero is two.
What are different conditions that could make vector product zero?
First of all, you have to define what you mean by "vector product".-- The "dot product" is zero if the vectors are perpendicular, regardless of their magnitudes.-- The "cross product" is zero if the vectors are collinear or opposite, regardless of their magnitudes.-- Perhaps when you say "product", you mean the "result" of two vectors, whicha mathematician or physicist would cal their "sum".The sum of two vectors is zero if their magnitudes are equal and their directionsdiffer by 180 degrees.An infinite number of other possibilities exist for a sum of zero, depending on themagnitudes and directions of two vectors.
Can the resultant of three vectors be zero also define is it possible for two vectors?
Yes. Any number of vectors, two or more, can result in zero, if their magnitudes and directions are just right. One vector can result in zero only if its magnitude is zero.
What is the minimum number of unequal forces whose vector sum can be zero is and why?
3
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.
Can resultant of 3 vectors be zero?
Sure. For one example, if their magnitudes are equal and their directions are spaced 120 degrees apart, then they add to zero. There are an infinite number of other sets of magnitudes and directions that add to zero, i.e. have a zero resultant.
What is the minimum number of unequal vectors that give a zero resultant?
Three One is obviously out. Two is out because if two unequal forces n and p act on an object the resultant with the minimum force in magnitude is |n - p|, which will never be 0 if n =/= p. Three can be easily resolved with a quick example. Imagine an object with three concurrent forces acting on it. Two forces, n = 3 N and p = 4 N, create an angle with each other such that the resultant is 5 N. 180 degrees from the resultant, a force, r = 5 N, is acting on the object. Thus three unequal vectors on an object can result in 0.
What is the minimum number of unequal forces whose vector sum can equal zero?
Three. Equal forces, two.
