{"id":455,"date":"2020-03-13T18:24:41","date_gmt":"2020-03-13T18:24:41","guid":{"rendered":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/?p=455"},"modified":"2021-06-23T21:07:42","modified_gmt":"2021-06-23T21:07:42","slug":"section-2-3-v2","status":"publish","type":"post","link":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2020\/03\/13\/section-2-3-v2\/","title":{"rendered":"Chapter 2: Vectors"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">2.3 Vector arithmetic and algebra<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">2.3.1 Scalar multiplication<\/h3>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_book_ch_2_2_1_lect\" width=\"800\" height=\"400\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h4 class=\"wp-block-heading\">Example<\/h4>\n\n\n\n<p>You may use the interactive below to observe how scalar multiplication works. You can adjust the&nbsp;<em>x<\/em> and <em>y&nbsp;<\/em>components of the vector, and also adjust the scalar&nbsp;<em>c<\/em>. After playing around with the interactive to get a sense of how it works, you should make some predictions: write down a vector on a piece of paper, and multiply it by some scalar. Then check your answer using the interactive.<\/p>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/a8c224ea-a5ce-4187-a6a5-4493d678be7f\" width=\"800\" height=\"650\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h4 class=\"wp-block-heading\">Practice<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_book_example_2_1\" width=\"800\" height=\"500\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h3 class=\"wp-block-heading\">2.3.2 Vector addition and&nbsp;subtraction<\/h3>\n\n\n\n<p>You will frequently need to add vectors together. There are two methods of adding vectors: graphically and algebraically.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Graphically<\/h4>\n\n\n\n<p>Place the \u201ctail\u201d of one vector at the origin. Place the \u201ctail\u201d of the other at the \u201ctip\u201d of the first. The sum of the two is the vector that points from the \u201ctail\u201d of the first vector to the \u201ctip\u201d of the second.<\/p>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/50913ed2-f1f9-4bde-ba41-e67a97201679\" width=\"800\" height=\"700\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<p>For subtraction, keep the magnitude (length) the same, but put it in the opposite direction.<\/p>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/fe4aebb5-db64-4016-ac84-fdedb97f98e9\" width=\"800\" height=\"700\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h4 class=\"wp-block-heading\">Algebraically<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_book_ch_2_2_2_lect\" width=\"800\" height=\"700\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h4 class=\"wp-block-heading\">Practice<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_book_ch2v2_qmas_prac\" width=\"800\" height=\"700\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n","protected":false},"excerpt":{"rendered":"<p>2.3 Vector arithmetic and algebra 2.3.1 Scalar multiplication Example You may use the interactive below to observe how scalar multiplication works. You can adjust the&nbsp;x and y&nbsp;components of the vector, and also adjust the scalar&nbsp;c. After playing around with the <span class=\"readmore\"><a href=\"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2020\/03\/13\/section-2-3-v2\/\">Continue Reading<\/a><\/span><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-455","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/455","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/comments?post=455"}],"version-history":[{"count":3,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/455\/revisions"}],"predecessor-version":[{"id":825,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/455\/revisions\/825"}],"wp:attachment":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/media?parent=455"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/categories?post=455"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/tags?post=455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}