In scalar product of vectors, the vector components are combined to give a scalar. The scalar product of two vectors is the product of the component of one vector (in the direction of the other vector) and the second vector. The scalar product is mostly used in Physics. The scalar product is also known as \u201cdot product\u201d.<\/p>\n
The mathematical definition of scalar product of two vectors a<\/em><\/strong> and b<\/em><\/strong> is denoted by a.b and is defined as follows.<\/p>\n a.b = |a| |b| Cos \u03b8, where \u03b8 is the angle between a<\/em><\/strong> and b<\/em><\/strong>.<\/p>\n Properties of scalar product:<\/span><\/strong><\/p>\n 1)\u00a0\u00a0\u00a0\u00a0\u00a0 a.b is a scalar.<\/p>\n 2)\u00a0\u00a0\u00a0\u00a0\u00a0 From the definition of scalar product, we have Cos \u03b8 = a.b\/|a| |b|<\/p>\n 3)\u00a0\u00a0\u00a0\u00a0\u00a0 a<\/em><\/strong> and b<\/em><\/strong> are orthogonal if a.b =0.<\/p>\n 4)\u00a0\u00a0\u00a0\u00a0\u00a0 a.b = b.a<\/p>\n 5)\u00a0\u00a0\u00a0\u00a0\u00a0 i.i=j.j=k.k=1, where i<\/em><\/strong>,j<\/em><\/strong> and k<\/em><\/strong> are mutually orthogonal unit vectors along x<\/em><\/strong>,y<\/em><\/strong> and z<\/em><\/strong>-axes.<\/p>\n 6)\u00a0\u00a0\u00a0\u00a0\u00a0 Dot product is distributive over addition.<\/p>\n i.e a.(b+c) = a.b+b.c<\/p>\n 7) For any scalar m<\/em><\/strong>, (ma).b = m(a.b)<\/p>\n 8) If a = a1<\/sub>i + a2<\/sub>j + a3<\/sub>k and b = b1<\/sub>i + b2<\/sub>j + b3<\/sub>k then a.b = a1<\/sub>b1<\/sub> + a2<\/sub>b2<\/sub> + a3<\/sub>b3<\/sub>.<\/p>\n (This is because i.j = j.k=k.i=0 because they are mutually orthogonal)<\/p>\n Example:<\/strong><\/p>\n If a = 3i + 2j + 5k and b = 2i \u2013 6j + 4k then find a.b<\/p>\n Solution:<\/strong><\/p>\n By property number 8,<\/p>\n a.b = 3*2 + 2*-6 + 5*4 = 6 -12 + 20 = 14.<\/p>\n <\/p>\n Do you also need help with French? Take a look at our French<\/a> tutoring services.<\/p>\n SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Parlier visit: Tutoring in Parlier . <\/a><\/p>\n","protected":false},"excerpt":{"rendered":" In scalar product of vectors, the vector components are combined to give a scalar. The scalar product of two vectors is the product of the component of one vector (in the direction of the other vector) and the second vector. The scalar product is mostly used in Physics. The scalar product is also known as […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[542,1268,1396,1412,1587],"class_list":["post-3296","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-dot","tag-orthogonal","tag-product","tag-properties","tag-scalar"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3296","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=3296"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3296\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=3296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=3296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=3296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}