{"id":4164,"date":"2012-10-05T20:00:31","date_gmt":"2012-10-05T20:00:31","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=4164"},"modified":"2014-12-02T08:32:00","modified_gmt":"2014-12-02T08:32:00","slug":"algebra-how-to-do-vector-addition","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/algebra-how-to-do-vector-addition\/","title":{"rendered":"Algebra: How to do Vector Addition"},"content":{"rendered":"

A Vector is a quantity which has both magnitude and direction.<\/p>\n

Example: <\/strong>Force, velocity, momentum etc.<\/p>\n

A vector is represented by a directed line segment. If the vector has the initial point P<\/em><\/strong> and final point Q<\/em><\/strong> then the vector is denoted by\u00a0\"\"<\/a>\u00a0 or PQ<\/em><\/strong>.<\/p>\n

The length of the vector is called its magnitude<\/em><\/strong> or length<\/em><\/strong> or modulus<\/em><\/strong>. The length of a vector PQ<\/em><\/strong> is denoted by |PQ|.<\/p>\n

Since a vector is not just a number they cannot be added just like numbers. There are some laws which can be used with the vector addition.<\/p>\n

Triangle law of addition:<\/h5>\n

Let a<\/em><\/strong> and b<\/em><\/strong> be any two vectors. Let O<\/em><\/strong> be any point. Let us assume that OA<\/em><\/strong> and OB<\/em><\/strong> are two line segments such that OA = a and AB = b. Join O<\/em><\/strong> and B<\/em><\/strong>. Then OB<\/em><\/strong> is defined as the sum of the vectors a<\/em><\/strong> and b<\/em><\/strong>.<\/p>\n

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

i.e. a+b = OA+OB = OB.<\/em><\/strong><\/p>\n

This is known as the triangle law of addition<\/em>.<\/p>\n

Parallelogram law of addition:<\/h5>\n

Let OA=a and OB = b. Complete the parallelogram OABC<\/em><\/strong> with OA<\/em><\/strong> and OB<\/em><\/strong> as sides. Since OC<\/em><\/strong> is parallel to AB<\/em><\/strong>, we get OC=AB. Thus we have OC=AB=b.<\/p>\n

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

So, OC= a+b = OA+AB = OA+OC.<\/em><\/strong><\/p>\n

i.e. The sum of two co-initial vectors OA<\/em><\/strong> and OC<\/em><\/strong> is given by OB<\/em><\/strong> where OB<\/em><\/strong> is the diagonal of the parallelogram OABC<\/em><\/strong> having OA<\/em><\/strong> and OC<\/em><\/strong> as the adjacent sides.<\/p>\n

This is known as parallelogram law of addition<\/em>.<\/p>\n

Polygon law of vectors:<\/h5>\n

Let OA = a<\/em><\/strong>, AB = b<\/em><\/strong>, BC= c<\/em><\/strong> and CD = d<\/em><\/strong>.<\/p>\n

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

a+b+c+d = OA+OB+OC+OD<\/p>\n

=OB +BC + CD<\/p>\n

= OC + CD<\/p>\n

=OD<\/p>\n

Thus the addition of vectors a<\/em><\/strong>,b<\/em><\/strong>,c<\/em><\/strong> and d<\/em><\/strong> is defined by OD<\/em><\/strong>.<\/p>\n

Properties of vector addition:<\/h5>\n

For any 3 vectors, a<\/em><\/strong>,b<\/em><\/strong> and c<\/em><\/strong>,<\/p>\n

1) a+b = b+a<\/p>\n

2) a+(b+c) = (a+b) +c<\/p>\n

3) a+0 = a<\/p>\n

4) a+ (-a)=0<\/p>\n

5) k(a+b)= ka+kb.<\/p>\n

6) a-b = a+ (-b)<\/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 Quebec visit: Tutoring in Quebec.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

A Vector is a quantity which has both magnitude and direction. Example: Force, velocity, momentum etc. A vector is represented by a directed line segment. If the vector has the initial point P and final point Q then the vector is denoted by\u00a0\u00a0 or PQ. The length of the vector is called its magnitude or […]<\/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":[50,1283,1356,1412,1853,1929],"class_list":["post-4164","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-addition","tag-parallelogram","tag-polygon","tag-properties","tag-triangle","tag-vector"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4164","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=4164"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4164\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}