Vector functions | Improve Society

If corresponding to each value of a scalar $u$ we associate a vector $\bold{A}$ , then $\bold{A}$ is called a function of $u$ denoted by $\bold{A}(u)$ . In there dimensions we can write $\bold{A}(u) = A_1(u)\bold{i} + A_2(u)\bold{j} + A_3(u)\bold{k}$ .

The function concept is easily extended. Thus if to each point $(x, y, z)$ there corresponds a vector $\bold{A}$ , then $\bold{A}$ is a function of $(x, y, z)$ , indicated by $\bold{A} = A_1(x, y, z)\bold{i} + A_2(x, y, z)\bold{j} + A_3(x, y, z)\bold{k}$ .

We sometimes say that a vector function $\bold{A}(x, y, z)$ defines a vector field since it associates a vector with each point of a region. Similarly $\phi(x, y, z)$ defines a scalar field since it associates a scalar with each point of a region.