{"id":4929,"date":"2014-03-04T06:05:09","date_gmt":"2014-03-03T21:05:09","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4929"},"modified":"2014-04-12T14:46:06","modified_gmt":"2014-04-12T05:46:06","slug":"components-of-a-vector","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4929","title":{"rendered":"Components of a vector"},"content":{"rendered":"
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Any vector \\bold{A} in 3 dimensions can be represented with initial point at the origin O<\/em> of a rectangular coordinate system. Let (A_1, A_2, A_3) be the rectangular coordinates of the terminal point of vector \\bold{A} with initial point at O<\/em>. The vectors A_1\\bold{i}, A_2\\bold{j} and A_3\\bold{k} are called the rectangular component vectors<\/em>, or simply component vectors<\/em>, of \\bold{A} in the x<\/em>, y<\/em> and z<\/em> directions respectively. A_1, A_2 and A_3 are called the rectangular components<\/em>, or simply components<\/em>, of \\bold{A} in the x<\/em>, y<\/em> and z<\/em> directions respectively. <\/p>\n

The sum or resultant of A_1\\bold{i}, A_2\\bold{j} and A_3\\bold{k} is the vector \\bold{A}, so that we can write<\/p>\n

\\bold{A} = A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k}\\cdots(1)<\/p>\n

The magnitude of \\bold{A} is<\/p>\n

A = |\\bold{A}| = \\sqrt{A_1^2 + A_2^2 + A_3^2}\\cdots(2)<\/p>\n

In particular, the position vector<\/em> or radius vector<\/em> \\bold{r} from O<\/em> to the point (x, y, z) is written<\/p>\n

\\bold{r} = x\\bold{i} + y\\bold{j} + z\\bold{k}\\cdots(3)<\/p>\n

and has magnitude r = |\\bold{r}| = \\sqrt{x^2 + y^2 + z^2}. <\/p>\n

\"Vector\"<\/a><\/p>\n<\/blockquote>\n