[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207744-en":3,"doc-seo-207744-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207744,13056712833777,"Paura","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",4,"Exam","AQA GCSE Maths - Vectors - Introduction to Vectors","Revision notes on AQA GCSE Maths vectors, focusing on core definitions and representation. Explains vectors as quantities with both magnitude and direction, limited here to two-dimensional vectors. Covers how vectors are shown using arrows, bold or underlined letters, and ordered starting/ending points. Introduces transformation-geometry translation vectors, including direction and order of points. Extends to representing vectors on coordinate grids, multiplying vectors by scalars, and adding or subtracting vectors using coordinate methods.","Head to www.savemyexams. com for more awesome resources  \n AQA GCSE Maths  \nVectors  \nContents  \n Introduction to Vectors  Working with Vectors  \nPage 1 of 27  \n© 2015 − 2025 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 What are vectors?  \n Avector is a type of number that has both a size anda direction  \n Here we only deal with two-dimensional vectors, although it is possible to have vectors with any number of dimensions  \nRepresenting vectors  \n Vectors are represented as arrows, with the arrowhead indicating the direction of the vector, and the length of the arrow indicating the vector’s magnitude (ie its size):  \nIn print vectors are usually represented by bold letters (as with vector a in the diagram above) , although in handwritten workings underlined letters are normally used, a.  \n Another way to indicate avector isto write its starting and ending points with an arrow symbol over the  \n􀀃⎯⎯⎯⎯􀀂  \ntop such as AB  \nPage 2 of 27  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n􀀃⎯⎯⎯⎯􀀂  \n Note that the order of the letters is important! Vector BA in the above diagram would point in the opposite direction (ie with its ‘tail’ at point B, and the arrowhead at point A) .  \nVectorsand transformation geometry  \nIn transformation geometry, translations are indicated in the form of a column vector:  \nPage 3 of 27  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n In the following diagram, Shape A has been translated six squarestothe right and 3 squares up to create Shape B  \n This transformation is indicated by the translation vector  63 ⎟ :  \nNote: ‘Vector’ is a word from Latin that means ‘carrier’  \n In this case, the vector ‘carries’ shape Ato shape B, so that meaning makes perfect sense! Vectorson a grid  \n You also need to be able to work with vectors on their own, outside of the transformation geometry context  \n When vectors are drawn on a grid (with or without x andy axes) , the vectors can be represented in the same (xy) column vector form as above  \nPage 4 of 27  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n⎛  \na = ⎜  \n⎝  \n3 4  \n⎞⎟ ⎛  \n⎟ , b = ⎜  \n⎠ ⎝  \n2  \n−4  \n⎞⎟ ⎛  \n⎟ , c = ⎜  \n⎠ ⎝  \n2 0  \n⎞  \n⎟⎟  \n⎟  \n⎠  \nMultiplying a vector by a scalar  \n A scalar is a number with a magnitude but no direction – ie the regular numbers you are used to using  \n When a vector is multiplied by a positive scalar, the magnitude of the vector changes, but its direction stays the same  \n If the vector is represented as a column vector, then each of the numbers in the column vector gets multiplied by the scalar  \nPage 5 of 27  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n⎛  \na = ⎜  \n⎝  \n4  \n−2  \n⎞⎟ ⎛⎠⎟ , 2 a =   \n2 × 4  \n2 × − 2  \n⎞ ⎛  \n⎟ ⎜  \n⎟ = ⎜  \n⎟ ⎜  \n⎠ ⎝  \n8  \n−4  \n⎞  \n⎟⎟  \n⎟ ,  \n⎠  \n 1  \n2 a =  \n⎛⎜  \n⎜⎜  \n⎝  \n0.5 × 4  \n0.5 × − 2  \n⎞ ⎛  \n⎟ ⎜  \n⎟ = ⎜  \n⎟ ⎜  \n⎠ ⎝  \n2  \n−1  \n⎞  \n⎟⎟  \n⎟  \n⎠  \n Note that multiplying by a negative scalar also changes the direction of the vector:  \nPage 6 of 27  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \n⎜⎛ 4 ⎞⎟ ⎜⎛ −4 ⎞⎟ ⎜⎛ −8 ⎞⎟  \na =  −2 ⎠⎟ , − a =  2 ⎠⎟ , − 2a =  4 ⎠⎟  \n Note in particular that vector-a is the the same size as vector a, but points in the opposite direction! Adding and subtracting vectors  \n Adding two vectors is de|ned geometrically, like this:  \nPage 7 of 27  \n© 2015 − 2025 Save My Exams, Ltd. · Revision Notes, Topic Questio","cbCaiepvZXSj3z6X","https://ap.wps.com/l/cbCaiepvZXSj3z6X","pdf",2784473,1,27,"English","en",105,"# Introduction to Vectors\n## Basic Vectors\n## Representing vectors\n## Vectors and transformation geometry\n## Vectors on a grid\n## Multiplying a vector by a scalar\n## Adding and subtracting vectors","[{\"question\":\"What is a vector in GCSE Maths?\",\"answer\":\"A vector is a type of number that has both a size (magnitude) and a direction. Here the notes focus on two-dimensional vectors.\"},{\"question\":\"How can vectors be represented?\",\"answer\":\"Vectors can be represented as arrows, with arrow length showing magnitude and arrowhead showing direction. They may also be written using bold letters or using an ordered pair of points like AB, where the order matters.\"},{\"question\":\"What happens when you multiply a vector by a scalar?\",\"answer\":\"Multiplying by a positive scalar changes the vector’s magnitude but keeps its direction. Multiplying by a negative scalar also reverses the direction.\"}]","AQA GCSE Maths - Vectors - Introduction to Vectors | PDF",1788600943,68,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"aqa-gcse-maths-vectors-introduction-to-vectors","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/aqa-gcse-maths-vectors-introduction-to-vectors/207744/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What is a vector in GCSE Maths?","Question",{"text":74,"@type":75},"A vector is a type of number that has both a size (magnitude) and a direction. Here the notes focus on two-dimensional vectors.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How can vectors be represented?",{"text":79,"@type":75},"Vectors can be represented as arrows, with arrow length showing magnitude and arrowhead showing direction. They may also be written using bold letters or using an ordered pair of points like AB, where the order matters.",{"name":81,"@type":72,"acceptedAnswer":82},"What happens when you multiply a vector by a scalar?",{"text":83,"@type":75},"Multiplying by a positive scalar changes the vector’s magnitude but keeps its direction. 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