{"id":20036,"date":"2022-09-21T08:05:48","date_gmt":"2022-09-21T08:05:48","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7836"},"modified":"2022-09-21T08:05:48","modified_gmt":"2022-09-21T08:05:48","slug":"coordinate-system-2","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/21\/coordinate-system-2\/","title":{"rendered":"Coordinate System 2"},"content":{"rendered":"\n

Figure 2 <\/strong>
              Drawing for Example 1.<\/p>\n\n\n\n

If the coordinates of point P<\/em> are ( x<\/em>, y<\/em>),<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

An algebraic vector<\/strong> is an ordered pair of real numbers. An algebraic vector that corresponds to standard geometric vector  is denoted as \u27e8 a, b<\/em>\u27e9 if terminal point P has coordinates of (a, b)<\/em>. The numbers a<\/em> and b<\/em> are called the components<\/strong> of vector \u27e8 a, b\u27e9<\/em> (see Figure 3 ).<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Figure 3 <\/strong>
              Components of a vector.<\/p>\n\n\n\n

If a, b, c<\/em>, and d<\/em> are all real numbers such that a<\/em> = c<\/em> and b<\/em> = d<\/em>, then vector v<\/strong> = \u27e8 a, b\u27e9<\/em> and vector u<\/strong> = \u27e8 c, d\u27e9<\/em> are said to be equal. That is, algebraic vectors with equal corresponding components are equal. If both components of a vector are equal to zero, the vector is said to be the zero vector<\/strong>. The magnitude<\/strong> of a vector v<\/strong> = \u27e8a, b\u27e9<\/em> is .<\/p>\n\n\n\n

Example 2:<\/strong> What is the magnitude of vector u<\/strong> = \u27e83, \u22125\u27e9?<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Vector addition<\/strong> is defined as adding corresponding components of vectors\u2014that is, if v<\/strong> = \u27e8 a, b\u27e9<\/em> and u<\/strong> = \u27e8c, d\u27e9<\/em>, then v<\/strong> + u<\/strong> = \u27e8a<\/em> + c, b<\/em> + d\u27e9<\/em> (Figure 4 ).<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Figure 4 <\/strong>
              Vector addition.<\/p>\n\n\n\n

Scalar multiplication<\/strong> is defined as multiplying each component by a constant\u2014that is, if v<\/strong> = \u27e8a, b\u27e9<\/em> and q<\/em> is a constant, then q<\/em> v<\/strong> = q\u27e8a, b\u27e9 = \u27e8qa, qb\u27e9<\/em>.<\/p>\n\n\n\n

Example 3:<\/strong> If v<\/strong> = \u27e88, \u22122\u27e9 and w<\/strong> = \u27e83, 7\u27e9 then find 5 v<\/strong> \u22122 w<\/strong>.<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

A unit vector<\/strong> is a vector whose magnitude is 1. A unit vector v<\/strong> with the same direction as a nonzero vector u<\/strong> can be found as follows:<\/p>\n\n\n\n

\"\"\/<\/figure>\n","protected":false},"excerpt":{"rendered":"

Figure 2               Drawing for Example 1. If the coordinates of point P are ( x, y), An algebraic vector is an ordered pair of real numbers. An algebraic vector that corresponds to standard geometric vector  is denoted as \u27e8 a, b\u27e9 if terminal point P has coordinates of (a, b). The numbers a and b are called the components of vector \u27e8 a, b\u27e9 (see Figure […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[716],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20036"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=20036"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20036\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=20036"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=20036"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=20036"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}