what is vector and units ?
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Vector____________
↪In mathematics and physics, a vector is an element of a vector space. For many specific vector spaces, the vectors have received specific names, which are listed below.
Vectors do have dimensions. Specifically, the dimension of a vector is (and always must be) the same as the dimension of its components. ... In your example, the position vector →r does indeed have units of length.
Units _______
↪A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity.
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A unit vector is a vector with length/magnitude 1. A basis is a set of vectors that span the vector space, and the set of vectors are linearly independent. A basis vector is thus a vector in a basis, and it doesn't need to have length 1.
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