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What is the smallest number of vectors that can be added to give a zero resultant?
Two vectors can be added to result in a zero resultant if they are equal in magnitude and opposite in direction.
Can the sum of of the magnitudes of two vectors ever be equal to the magnitudes of the sum of these two vectors?
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|.
What are different conditions that could make vector product zero?
The vector product (cross product) of two vectors will be zero when the vectors are parallel or antiparallel to each other. This means the vectors are either pointing in the same direction (parallel) or in opposite directions (antiparallel).
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 many equal vectors should be added to get a null vector?
To get a null vector, you need to add at least two equal vectors together. Adding any number of equal vectors will always result in a vector that is parallel to the original vector, but to get a null vector the magnitudes of two equal vectors must cancel each other out.
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.
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 is the smallest number of vectors that can be added to give a zero resultant?
Two vectors can be added to result in a zero resultant if they are equal in magnitude and opposite in direction.
Can the sum of of the magnitudes of two vectors ever be equal to the magnitudes of the sum of these two vectors?
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|.
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
What are different conditions that could make vector product zero?
The vector product (cross product) of two vectors will be zero when the vectors are parallel or antiparallel to each other. This means the vectors are either pointing in the same direction (parallel) or in opposite directions (antiparallel).
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.
