unit of vector means
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Formula
\mathbf {\hat {u}}= \frac{ \mathbf {u}}{\mathbf {|u|}}
\mathbf {\hat {u}} = normalized vector
\mathbf {u} = non-zero vector
\mathbf {|u|} = norm (or length) of u
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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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