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Two vectors: no. Three vectors: yes.
In order for two vectors to add up to zero:-- their directions must be exactly opposite-- their magnitudes must be exactly equal
No.A vector space is a set over a field that has to satisfy certain rules, called axioms. The field in question can be Z2 (see discussion), but unlike a field, a vector's inverse is distinct from the vector. Therefore, in order to satisfy the "inverse elements of addition" axiom for vector spaces, a vector space must minimally (except if it is the null space) have three vectors, v, 0, and v-1. The null space only has one vector, 0.Field's can allow for two distinct elements, unlike vector spaces, because for any given element of a field, for example a, a + (-a) = 0 meets the inverse axiom, but a and -a aren't required to be distinct. They are simply scalar magnitudes, unlike vectors which can often be thought of as having a direction attached to them. That's why the vectors, v and -v are distinct, because they're pointing in opposite directions.
If they are equal in magnitude but act in opposite directions.
Assuming you mean sum and not some, the answer is No.
When two vectors sum to zero, they must be equal in magnitude but opposite in direction. This relationship is known as the vectors being antiparallel.
Two vectors: no. Three vectors: yes.
The range of possible values of the resultant of two vectors is from the magnitude of the difference of the magnitudes of the two vectors to the sum of the magnitudes of the two vectors. This range occurs when the two vectors are in the same direction or in opposite directions, respectively.
Yes, it is possible to add any two vectors as long as they have the same number of dimensions. The result of adding two vectors is a new vector whose components are the sum of the corresponding components of the original vectors.
Their magnitudes are exactly equal, and their directions are exactly opposite.
In order for two vectors to add up to zero:-- their directions must be exactly opposite-- their magnitudes must be exactly equal
no!!!only scalars and scalars and only vectors and vectors can be added.
No.A vector space is a set over a field that has to satisfy certain rules, called axioms. The field in question can be Z2 (see discussion), but unlike a field, a vector's inverse is distinct from the vector. Therefore, in order to satisfy the "inverse elements of addition" axiom for vector spaces, a vector space must minimally (except if it is the null space) have three vectors, v, 0, and v-1. The null space only has one vector, 0.Field's can allow for two distinct elements, unlike vector spaces, because for any given element of a field, for example a, a + (-a) = 0 meets the inverse axiom, but a and -a aren't required to be distinct. They are simply scalar magnitudes, unlike vectors which can often be thought of as having a direction attached to them. That's why the vectors, v and -v are distinct, because they're pointing in opposite directions.
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.
If they are equal in magnitude but act in opposite directions.
monkeys
Assuming you mean sum and not some, the answer is No.