{"id":5006,"date":"2014-03-20T06:05:18","date_gmt":"2014-03-19T21:05:18","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5006"},"modified":"2014-08-01T18:45:53","modified_gmt":"2014-08-01T09:45:53","slug":"vector-functions","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5006","title":{"rendered":"Vector functions"},"content":{"rendered":"
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If corresponding to each value of a scalar u we associate a vector \\bold{A}, then \\bold{A} is called a function<\/em> 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}. <\/p>\n

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}. <\/p>\n

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