Vector Analysis and Vector Fields

A vector function of a scalar variable is a vector \( {\vec{\text{a}}} \) whose components are real functions of t: \( {\vec{\text{a}}} = {\vec{\text{a}}}(t) = a_{x} (t ) {\vec{\text{e}}}_{x} + a_{y} (t ) {\vec{\text{e}}}_{y} + a_{z} (t ) {\vec{\text{e}}}_{z} . \) The notions of limit, continuity, differentiability are defined componentwise for the vector \( {\vec{\text{a}}}(t) \).