{"id":4174,"date":"2012-10-05T20:00:44","date_gmt":"2012-10-05T20:00:44","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=4174"},"modified":"2014-12-02T08:32:00","modified_gmt":"2014-12-02T08:32:00","slug":"algebra-how-to-do-vector-product-cross-product","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/algebra-how-to-do-vector-product-cross-product\/","title":{"rendered":"Algebra: How to do Vector Product (Cross Product)"},"content":{"rendered":"

In vector product of vectors, the vector components are combined to give a vector. The vector product of two vectors is a vector which is perpendicular to both the given vectors. The vector product is mostly used in Physics<\/a>. The vector product is also known as \u201ccross product\u201d.<\/p>\n

The mathematical definition of vector product of two vectors a<\/em><\/strong> and b<\/em><\/strong> is denoted by axb and is defined as follows.<\/p>\n

axb = |a| |b| Sin \u03b8, where \u03b8 is the angle between a<\/em><\/strong> and b<\/em><\/strong>.<\/p>\n

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

Properties of vector product:<\/span><\/strong><\/p>\n

1)\u00a0\u00a0\u00a0\u00a0\u00a0 axb is a vector.<\/p>\n

2)\u00a0\u00a0\u00a0\u00a0\u00a0 From the definition of vector product, we have Sin \u03b8 = |axb|\/|a| |b|<\/p>\n

3)\u00a0\u00a0\u00a0\u00a0\u00a0 a<\/em><\/strong> and b<\/em><\/strong> are parallel if axb =0.<\/p>\n

4)\u00a0\u00a0\u00a0\u00a0\u00a0 axb = -bxa<\/p>\n

5)\u00a0\u00a0\u00a0\u00a0\u00a0 ixi=jxj=kxk=0, 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 Cross product is distributive over addition.<\/p>\n

i.e ax(b+c) = axb+bxc<\/p>\n

7) For any vector m<\/em><\/strong>, (ma)xb = m(axb)<\/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 axb can be expressed as a determinant as follows.<\/p>\n

axb = \"\"<\/a><\/strong><\/strong><\/strong><\/p>\n

(This is because ixj = k, j.k= i and k.i=j)<\/p>\n

Example:<\/strong><\/p>\n

If a = 3i + 2j + 5k and b = 2i \u2013 6j + 4k then find axb<\/p>\n

Solution:<\/strong><\/p>\n

By property number 8,<\/p>\n

axb = \"\"<\/a><\/strong><\/strong>\u00a0= i ( 8-4) \u2013 j (12-10) + k (-18 -4) = 4i =2j -22k<\/strong><\/p>\n

 <\/p>\n

Do you also need help with Standardized Tests? Take a look at our Test Prep tutoring services.<\/a><\/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 Saskatchewan visit: Tutoring in Saskatchewan.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

In vector product of vectors, the vector components are combined to give a vector. The vector product of two vectors is a vector which is perpendicular to both the given vectors. The vector product is mostly used in Physics. The vector product is also known as \u201ccross product\u201d. The mathematical definition of vector product of […]<\/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":[431,483,1280,1396,1412,1929],"class_list":["post-4174","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-cross","tag-determinant","tag-parallel","tag-product","tag-properties","tag-vector"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4174","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=4174"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4174\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}