{"id":698,"date":"2021-05-06T12:16:16","date_gmt":"2021-05-06T06:46:16","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=698"},"modified":"2021-10-30T07:40:44","modified_gmt":"2021-10-30T07:40:44","slug":"what-are-vectors","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-are-vectors\/","title":{"rendered":"What Are Vectors?"},"content":{"rendered":"\n<p>The study of vectors is useful in engineering mathematics, physics, civil engineering, research fields etc.<\/p>\n\n\n\n<p>Vector calculus was developed by Josiah Willard Gibbs around the 19th century.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Definition-&nbsp;<\/strong><\/h2>\n\n\n\n<p>When a quantity has magnitude as well as direction (both) is called a vector.<\/p>\n\n\n\n<p>Note- A physical quantity having magnitude only, is known as scalar.<\/p>\n\n\n\n<p><strong>For example-<\/strong> Acceleration, force, velocity, momentum, magnetic induction etc. are the vector quantities.<\/p>\n\n\n\n<p>and density, speed, energy, mass, volume, temperature etc. are the examples of scalar quantities.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Characteristics of vectors-<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>A vector quantity has both direction and magnitude.<\/li><li>We use an arrow sign on the head of the symbol we use for vector quantity.<\/li><li>Vectors do not follow the algebra rules when they are added or subtracted.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Addition of vectors <\/strong>&#8211;&nbsp;<\/h2>\n\n\n\n<p>Suppose we have two vectors <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/de5AxMADYTI5BKWGHW_S-4YODxD3VrIsqcfODLL0cj2IV8h9TOsLcKVVXyuXpLBKLtM0G9vIWk3OxpRE6S8tk8SmG062t7D7OCVxX05VbJxWRsSImjIZtmy1lCn2RyNKA8WkXmNv\" width=\"24\" height=\"24\">and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/dtVKuwwk8Stbk_Rv2vBRe-GWzLespW1UbEImkgUXcRlACVliXgEDnj-EH_ViP5pC0DcvqoTaexDOvjzEkWWS7ifY_RqfXt00vt6rP_AwPZZ_oFE7cn6DOamS7iYKOiFHf1HeSZPG\" width=\"19\" height=\"24\">then we can add these two by joining them head to tail as below-<\/p>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/fvyhV8zmpGwixcdMiznXXdZ4R0qT-JFsIhJDw3jFMAE2zSCfMdqS3WtRU7H3F0m0U7UF6EuOGGIKcjkQXsFjAxmijQF-BIA7h_ykSWtHWaY2E6hglSZq7zNF642KIR2q19rhBBDw\" width=\"372\" height=\"225\"><\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/PZW5QwGa2glrC141XMIzcvwfydfE8yjkbtoaYRZGTt2Ks-ZyxWto2QdTNNlMjeSA7p7fYMGAKHEkdcl9u74yiBV7CDX6we7e_Nl7Bd6iN8PxOoOpSQkz2AXkzbTSTcEZI9GrTTOb\" width=\"31\" height=\"24\">is called the sum of vectors <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/de5AxMADYTI5BKWGHW_S-4YODxD3VrIsqcfODLL0cj2IV8h9TOsLcKVVXyuXpLBKLtM0G9vIWk3OxpRE6S8tk8SmG062t7D7OCVxX05VbJxWRsSImjIZtmy1lCn2RyNKA8WkXmNv\" width=\"24\" height=\"24\">and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/dtVKuwwk8Stbk_Rv2vBRe-GWzLespW1UbEImkgUXcRlACVliXgEDnj-EH_ViP5pC0DcvqoTaexDOvjzEkWWS7ifY_RqfXt00vt6rP_AwPZZ_oFE7cn6DOamS7iYKOiFHf1HeSZPG\" width=\"19\" height=\"24\">.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/e4PeBQ_JzxRJkAMw6A4Z8lo0q-dA6S4jU3xvaBYOYLggKwajob811e8mKdrPp_GiX73G0qViGrQAX3q1VHoc9US61pkL-nWYLNiB-AwC1505sipz7u9qSVH18OmuicHTWzrUDAyg\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>OR<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/aFlWlcAc1WGU5aQUqquWMNpstrneuENPvRqrc9dmai56Y-8AKN4s1MeGY2xweVHAq432ayKqQZ4lZ6LtAKyNA6UXkcc1-jC9MhC0OcvA42cvpJ89LKr8BElhW-8ILgYsyrzi9scj\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p><strong>Note-&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Addition of vectors satisfies commutative and associative law.<\/li><li>The arrows show directions of the vector.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Subtraction of vectors-&nbsp;<\/strong><\/h2>\n\n\n\n<p>We can subtract one vector from another by reversing the direction of vector that we need to subtract and adding them-<\/p>\n\n\n\n<p>See below-<\/p>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/GpBjlsGb9pf_L-7cu87wr3_VHr0QMa0KcvOBFcRS2lcG7EXExZ8dksiid_wBZtEhLVQUR2RTRrnGgM2oLF4M35Nn9YHmE4stVjNZmXIZh09xgRmIbusast7XvpHDPTFJCsTnmrq9\" width=\"257\" height=\"180\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Unit vector-<\/strong>&nbsp;<\/h2>\n\n\n\n<p>Suppose a vector is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/AUHXij6KdwLRTk_o1F2FbIbrnEaw6CeJpIrncJbFd_lYOsapdlSk-cNnOjgvqmtnMmTpdxE5wvSBF-AXJQLSHHk6VZU_s23bcDpevWoxHwMyCR6AUbbH4ELVuu11rSjaehsCULyy\" width=\"100\" height=\"24\"> then the unit vector is defined as-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/tsJNvo47gtX1XbhlDBAIZgg12c1o03ifVvGQYgt5uciDqYwf69We1KfQxBhLlFoE6quHLiukvxTx8aNs6BX7mIo4P7D4j402twYSUqlmqJzT6HLTafbusVPu4Fe16giWj3cGUN2l\" alt=\"\" width=\"209\" height=\"56\"\/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Product of two vectors-&nbsp;<\/strong><\/h2>\n\n\n\n<p>There are two types of product of two vectors, the first one is scalar product or dot product and other is vector product or cross product.<\/p>\n\n\n\n<p>The scalar or dot product is defined as-<\/p>\n\n\n\n<p><strong>Scalar product-&nbsp;<\/strong><\/p>\n\n\n\n<p>Suppose there are two vectors <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/de5AxMADYTI5BKWGHW_S-4YODxD3VrIsqcfODLL0cj2IV8h9TOsLcKVVXyuXpLBKLtM0G9vIWk3OxpRE6S8tk8SmG062t7D7OCVxX05VbJxWRsSImjIZtmy1lCn2RyNKA8WkXmNv\" width=\"24\" height=\"24\"> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/dtVKuwwk8Stbk_Rv2vBRe-GWzLespW1UbEImkgUXcRlACVliXgEDnj-EH_ViP5pC0DcvqoTaexDOvjzEkWWS7ifY_RqfXt00vt6rP_AwPZZ_oFE7cn6DOamS7iYKOiFHf1HeSZPG\" width=\"20\" height=\"25\">then their scalar product is-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"181\" height=\"39\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2021\/04\/image-2.png?resize=181%2C39&#038;ssl=1\" alt=\"\" class=\"wp-image-701\"\/><\/figure><\/div>\n\n\n\n<p> <\/p>\n\n\n\n<p><strong>Note-<\/strong>&nbsp;<\/p>\n\n\n\n<p>The dot product is commutative &#8211;<\/p>\n\n\n\n<p class=\"has-text-align-center\">&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/de5AxMADYTI5BKWGHW_S-4YODxD3VrIsqcfODLL0cj2IV8h9TOsLcKVVXyuXpLBKLtM0G9vIWk3OxpRE6S8tk8SmG062t7D7OCVxX05VbJxWRsSImjIZtmy1lCn2RyNKA8WkXmNv\" width=\"24\" height=\"24\">.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/dtVKuwwk8Stbk_Rv2vBRe-GWzLespW1UbEImkgUXcRlACVliXgEDnj-EH_ViP5pC0DcvqoTaexDOvjzEkWWS7ifY_RqfXt00vt6rP_AwPZZ_oFE7cn6DOamS7iYKOiFHf1HeSZPG\" width=\"20\" height=\"25\">=<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/dtVKuwwk8Stbk_Rv2vBRe-GWzLespW1UbEImkgUXcRlACVliXgEDnj-EH_ViP5pC0DcvqoTaexDOvjzEkWWS7ifY_RqfXt00vt6rP_AwPZZ_oFE7cn6DOamS7iYKOiFHf1HeSZPG\" width=\"20\" height=\"25\">.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/de5AxMADYTI5BKWGHW_S-4YODxD3VrIsqcfODLL0cj2IV8h9TOsLcKVVXyuXpLBKLtM0G9vIWk3OxpRE6S8tk8SmG062t7D7OCVxX05VbJxWRsSImjIZtmy1lCn2RyNKA8WkXmNv\" width=\"24\" height=\"24\"><\/p>\n\n\n\n<p><strong>Vector product &#8211;<\/strong><\/p>\n\n\n\n<p>The vector product or cross product is defined as-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"209\" height=\"49\" src=\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2021\/04\/image-4.png?resize=209%2C49&#038;ssl=1\" alt=\"\" class=\"wp-image-703\"\/><\/figure><\/div>\n\n\n\n<p>here <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/OJlxb9GlDUqSXY5L3z1_edQi-yKPlDkCE0tgBlGXBfva3A6hct48OxBQqY5zstPS2HnGZGV3OxNS03TUG74W2GinPl0Y0IfErfjFIPnzL-W0KWyKtTpWxP7D5zU4OdpWZpq0k34S\" width=\"20\" height=\"32\">is the unit vector in the direction of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/de5AxMADYTI5BKWGHW_S-4YODxD3VrIsqcfODLL0cj2IV8h9TOsLcKVVXyuXpLBKLtM0G9vIWk3OxpRE6S8tk8SmG062t7D7OCVxX05VbJxWRsSImjIZtmy1lCn2RyNKA8WkXmNv\" width=\"24\" height=\"24\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/dtVKuwwk8Stbk_Rv2vBRe-GWzLespW1UbEImkgUXcRlACVliXgEDnj-EH_ViP5pC0DcvqoTaexDOvjzEkWWS7ifY_RqfXt00vt6rP_AwPZZ_oFE7cn6DOamS7iYKOiFHf1HeSZPG\" width=\"20\" height=\"25\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>When a quantity has magnitude as well as direction is called a vector.<\/p>\n","protected":false},"author":3,"featured_media":946,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-698","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What Are Vectors? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"The study of vectors is useful in engineering mathematics, physics, civil engineering, research fields etc. It was developed by J.W Gibbs.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.goseeko.com\/blog\/what-are-vectors\/\" \/>\n<meta property=\"og:locale\" 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