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A vector space is a set of all points that can be generated by a linear combination of some integer number of vectors. A field is an abstract mathematical construct that is basically a set elements that form an abelian group under two binary operations, with the distributive property. Examples:
Euclidean space(x,y,z) is a vector space.
The rational and real numbers form a field with regular addition and multiplication.
Also, every set of congruence classes formed under a prime integer (mod algebra) is a field.
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Can a vector space have exactly two distinct vectors in it?
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.
Is magnetic field line scalar or vector quantity?
Vector.
The direction of the electric field vector is defined as?
Direction of the electric field vector is the direction of the force experienced by a charged particle in an external electric field.
Which of this two quantities is not a vector quantity magnetic field or charge?
Charge is not a vector.
Is magnetic field strength a vector quantity?
When one refers to the strength of a magnetic field, they're usually referring to the scalar magnitude of the magnetic field vector, so no.
