[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-206934-105":59,"doc-detail-206934-en":124},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":117,"head_meta":119,"extra_data":121,"updated_unix":123},105,"en","edexcel-gcse-maths-foundation-vectors","Edexcel GCSE Maths - Foundation - Vectors","","Revision notes for Edexcel GCSE Maths Foundation covering vectors: what column vectors represent, how to add and subtract them by combining top and bottom components, and how to multiply vectors by scalars. Includes worked guidance on forming a single column-vector expression using order of operations, plus vector diagrams for visual representation. Explains magnitude and direction, notation such as AB, and drawing vectors on grids by using correct lengths, directions, and handling negatives and zeroes.",{"@graph":69,"@context":116},[70,84,99],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/edexcel-gcse-maths-foundation-vectors/206934/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Đào","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What is a column vector used to describe?","Question",{"text":106,"@type":107},"A column vector describes how to get from one point to another point, also called a translation vector.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"How do you add or subtract column vectors?",{"text":111,"@type":107},"Add or subtract the top numbers together and the bottom numbers together separately, then combine the results into a new column vector.",{"name":113,"@type":104,"acceptedAnswer":114},"What happens when you multiply a vector by a scalar?",{"text":115,"@type":107},"A positive scalar keeps the direction the same and scales the length. A negative scalar reverses the direction and scales the length by the absolute value.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},206934,1788596891,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":133,"language":134,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":135,"faqs":136,"seo_title":137,"seo_description":67,"update_tm":123,"read_time":138},1374402968488,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Head to www.savemyexams. com for more awesome resources  \n Edexcel GCSE Maths: Foundation  \nVectors  \nContents  \n Introduction to Vectors  Working with Vectors  \nPage 1 of 17  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nIntroduction to Vectors  \nBasic Vectors  \nWhat are column vectors?  \n A column vector can be used to describe how to get from one point to another point  \n This is also called a translation vector  \n⎜⎛ 6 ⎞⎟  \n  3 ⎠⎟ means 6 units to the right and 3 units up  \nHow do I add and subtract column vectors?  \n Adding and subtracting vectors is done by looking atthe top numbers and bottom numbers separately  \n To add column vectors  \n Add the top numbers together  \n Add the bottom numbers together  \n⎜⎛ 5 ⎞⎟ ⎛ 3 ⎞ ⎛ 5 + 3 ⎞ ⎛ 8 ⎞  \n  2 ⎠⎟ +  −1 ⎠⎟ =  2 + (−1) ⎠⎟ =  1 ⎠⎟  \n To subtract column vectors  \n Subtract the second top number from the |rst  \n Subtract the second bottom number from the |rst  \nPage 2 of 17  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n⎛⎜  \n⎜⎜  \n⎝  \n5  \n2  \n⎞ ⎛  \n⎟ ⎜  \n⎟ − ⎜  \n⎟ ⎜  \n⎠ ⎝  \n3  \n−1  \n⎞ ⎛  \n⎟ ⎜  \n⎟ = ⎜  \n⎟ ⎜  \n⎠ ⎝  \n5 − 3  \n2 − (−1)  \n⎞ ⎛  \n⎟ ⎜  \n⎟ = ⎜  \n⎟ ⎜  \n⎠ ⎝  \n2 3  \n⎞  \n⎟⎟  \n⎟  \n⎠  \nHow do I multiply a vector by a scalar?  \n A scalar is number not a vector  \n It does not have a direction  \n To multiply a column vector by a scalar  \n Multiply the top number by the scalar  \n Multiply the bottom number by the scalar  \n3  2 ⎞⎟ =  3 × 2 ⎞⎟ =  6 ⎞⎟⎝ −1 ⎠  3 × (−1) ⎠⎟  −3 ⎠⎟  \nHow do I write an expression asa single column vector?  \n You need to follow the order of operations  \n⎜⎛ 5 ⎞⎟ ⎜⎛ 3 ⎞⎟  \n2 ⎜ ⎟ + 5⎜ ⎟⎝ 2 ⎠ ⎝ −1 ⎠  \n STEP 1  \nMultiply each vector by the scalar in front of it  \n⎜⎛ 2 × 5 ⎞⎟ ⎜⎛ 5 × 3 ⎞⎟ ⎜⎛ 10 ⎞⎟ ⎜⎛  \n  2 × 2 ⎠⎟ +  5 × (−1) ⎠⎟ =  4 ⎠⎟ +   \n STEP 2  \nAdd or subtract the new column vectors  \n⎜⎛ 10 + 15 ⎞⎟ ⎜⎛ 25 ⎞⎟  \n  4 + (−5) ⎠⎟ =  −1 ⎠⎟  \n15  \n−5  \n⎞  \n⎟⎟  \n⎟  \n⎠  \nPage 3 of 17  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n\n|  Worked example |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| ⎛\u003Cbr>a = ⎜\u003Cbr>⎝ | p 3 | ⎞ ⎛\u003Cbr>⎟ and b = ⎜\u003Cbr>⎠ ⎝ | −2\u003Cbr>1 | ⎞\u003Cbr>⎟⎟\u003Cbr>⎟ .\u003Cbr>⎠ |  |  |  |\n| ⎛ 4 ⎞\u003Cbr>Given that 2 a + 3b = ⎜ ⎟ ,⎝q ⎠ |  |  |  |  | |nd the value of p and the value of q . |  |  |\n| Write the left-side side as one vector\u003Cbr>Multiple each vector by the scalar in front of it |  |  |  |  |  |  |  |\n| Add the vectors together\u003Cbr>The top components are equal Form and solve an equation\u003Cbr>The bottom components are equal |  |  |  |  |  | \u003Cbr>|  |\n|  |  |  |  |  |  | | and |\n\nPage 4 of 17  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nVector Diagrams  \nHow can I represent a vector visually?  \n A vector has both a size (magnitude) anda direction  \n You need to draw a lineto show the size of the vector  \n You also need to draw anarrow to show the direction of the vector  \nVectors are written in bold when typed to show that they are a vector and not a scalar  \n When writing avector in an exam you should underline the letter to show it is a vector  \n a when typedand  a when handwritten  \n You will not lose marks if you forget to underline vectors  \n􀀃⎯⎯⎯⎯􀀂  \n Ifa vector starts atA and ends atB we can write itas AB  \n Here the arrow will point toward B  \n􀀃⎯⎯⎯⎯􀀂  \n Vector BA will have the same length but point toward A  \nPage 5 of 17  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nHow do I draw avectorona grid?  \n You can draw a vector anywhere on a grid  \n Just make sure it hasthe correct length and the correct direc","cbCaivHvHtSnOtQu","https://ap.wps.com/l/cbCaivHvHtSnOtQu","pdf",1639543,17,"English","# Introduction to Vectors\n## Basic Vectors\n## Vector Diagrams\n## Working with Vectors","[{\"question\":\"What is a column vector used to describe?\",\"answer\":\"A column vector describes how to get from one point to another point, also called a translation vector.\"},{\"question\":\"How do you add or subtract column vectors?\",\"answer\":\"Add or subtract the top numbers together and the bottom numbers together separately, then combine the results into a new column vector.\"},{\"question\":\"What happens when you multiply a vector by a scalar?\",\"answer\":\"A positive scalar keeps the direction the same and scales the length. A negative scalar reverses the direction and scales the length by the absolute value.\"}]","Edexcel GCSE Maths - Foundation - Vectors | PDF",43]