[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523547-105":59,"doc-detail-523547-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","three-dimensional-vector-basics-kuta-infinite-precalculus-worksheet","Three Dimensional Vector Basics - kuta Infinite Precalculus - Worksheet","","Worksheet focused on three-dimensional vectors in component form and linear combination. Students convert given vectors like CD, AB, and RS into x-, y-, and z-components, then determine magnitudes using standard distance formulas. Additional tasks address writing vectors using i, j, k notation, identifying head and tail points across octants, and generating possible integer component combinations that satisfy a fixed magnitude of 6. Critical thinking questions extend interpretation beyond computation.",{"@graph":69,"@context":122},[70,84,105],{"@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/three-dimensional-vector-basics-kuta-infinite-precalculus-worksheet/523547/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/three-dimensional-vector-basics-kuta-infinite-precalculus-worksheet/523547.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you write a given 3D vector in component form?","Question",{"text":112,"@type":113},"Break the vector into its x-, y-, and z-components from the ordered coordinate representation provided (e.g., C = (x,y,z)).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does it mean to write a vector as a linear combination?",{"text":117,"@type":113},"Express the vector using scalar multiples of i, j, and k (or the given basis directions), matching its components along each axis.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you find vectors that have magnitude 6 with integer components?",{"text":121,"@type":113},"List integer x, y, and z values whose squares add up to 6^2, then provide all sign combinations that satisfy the magnitude condition.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523547,1791753317,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Precalculus Name   \nThree Dimensional Vector Basics Date  Period   \nWrite each vector in component form.  \n1) CD  where C = (􀀕 , 􀀐􀀖 , 􀀖) D = (􀀐􀀚 , 􀀔 , 􀀕) 2) AB  where A = (􀀓 , 􀀐􀀕 , 􀀐􀀔) B = (􀀐􀀕 , 􀀐􀀖 , 􀀚 )  \nWrite each vector as a linear combination.  \n3) RS  where R = (􀀐􀀗 , 􀀜 , 􀀐􀀜) S = (􀀚 , 􀀜 , 􀀛) 4) CD  where C = (􀀔 , 􀀐􀀛 , 􀀐􀀚) D = (􀀔 , 􀀔 , 􀀓)  \nFind the magnitude of each vector.  \n5) v 􀀠 􀀕 i~~ ~~ 􀀎 􀀚j 􀀎 􀀘 k 6) RS  where R = (􀀙 , 􀀘 , 􀀐􀀛) S = (􀀔 , 􀀖 , 􀀐􀀜)  \n7) u 􀀠 􀀐􀀗 , 􀀐􀀙 , 􀀜 8) u 􀀠 􀀐􀀚 i  􀀐 j 􀀐 k   \nCritical thinking questions:  \n9) Find the head and tail points for  \nAB 􀀠 􀀛 , 􀀐􀀔 , 􀀕 that starts in octant VI and ends in octant V.  \n10) What are the possible integer x, y, and z components of a three-dimensional vector with a magnitude of 6?  \nKuta Software-Infinite Precalculus  \nThree Dimensional Vector Basics  \nWrite each vector in component form.  \n1) CD  where C = (􀀕 , 􀀐􀀖 , 􀀖) D = (􀀐􀀚 , 􀀔 , 􀀕)  \n􀀐􀀜 , 􀀗 , 􀀐􀀔   \nName  Date  Period   \n2) AB  where A = (􀀓 , 􀀐􀀕 , 􀀐􀀔) B = (􀀐􀀕 , 􀀐􀀖 , 􀀚 )  \n􀀐􀀕 , 􀀐􀀔 , 􀀛  \nWrite each vector as a linear combination.  \n3) RS  where R = (􀀐􀀗 , 􀀜 , 􀀐􀀜) S = (􀀚 , 􀀜 , 􀀛) 4) CD  where C = (􀀔 , 􀀐􀀛 , 􀀐􀀚) D = (􀀔 , 􀀔 , 􀀓)  \n􀀔􀀔 i  􀀎 􀀔􀀚k 􀀜j 􀀎 􀀚k   \nFind the magnitude of each vector.  \n5) v 􀀠 􀀕 i~~ ~~ 􀀎 􀀚j 􀀎 􀀘 k 6) RS  where R = (􀀙 , 􀀘 , 􀀐􀀛) S = (􀀔 , 􀀖 , 􀀐􀀜)  \n􀀚􀀛 􀁼 􀀛􀀑􀀛􀀖􀀕 􀀖􀀓 􀁼 􀀘􀀑􀀗􀀚􀀚  \n7) u 􀀠 􀀐􀀗 , 􀀐􀀙 , 􀀜 8) u 􀀠 􀀐􀀚 i  􀀐 j 􀀐 k   \n􀀔􀀖􀀖 􀁼 􀀔􀀔􀀑􀀘􀀖􀀖 􀀘􀀔 􀁼 􀀚􀀑􀀔􀀗􀀔  \nCritical thinking questions:  \n9) Find the head and tail points for  \nAB 􀀠 􀀛 , 􀀐􀀔 , 􀀕 that starts in octant VI and ends in octant V.  \nMultiple Answers:  \nA = (􀀐􀀚 , 􀀙 , 􀀐􀀗) B = (􀀔 , 􀀘 , 􀀐􀀕)  \n10) What are the possible integer x, y, and z components of a three-dimensional vector with a magnitude of 6?  \nx = ± 􀀗 , y = ± 􀀗 , z = ± 􀀕  \nx = ± 􀀗 , y = ± 􀀕 , z = ± 􀀗  \nx = ± 􀀕 , y = ± 􀀗 , z = ± 􀀗  \nx = ± 􀀙 , y 􀀠 􀀓 , z 􀀠 􀀓  \nx 􀀠 􀀓 , y = ± 􀀙 , z 􀀠 􀀓  \nx 􀀠 􀀓 , y 􀀠 􀀓 , z = ± 􀀙  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaitWGTcychkwW","https://ap.wps.com/l/cbCaitWGTcychkwW","pdf",27084,"English","# Write each vector in component form\n## Write each vector as a linear combination\n## Find the magnitude of each vector\n## Critical thinking questions\n## Multiple Answers","[{\"question\":\"How do you write a given 3D vector in component form?\",\"answer\":\"Break the vector into its x-, y-, and z-components from the ordered coordinate representation provided (e.g., C = (x,y,z)).\"},{\"question\":\"What does it mean to write a vector as a linear combination?\",\"answer\":\"Express the vector using scalar multiples of i, j, and k (or the given basis directions), matching its components along each axis.\"},{\"question\":\"How do you find vectors that have magnitude 6 with integer components?\",\"answer\":\"List integer x, y, and z values whose squares add up to 6^2, then provide all sign combinations that satisfy the magnitude condition.\"}]","Three Dimensional Vector Basics - kuta Infinite Precalculus - Worksheet | PDF",1791426989]