[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523548-105":59,"doc-detail-523548-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-operations-3d-vector-operations-worksheet-component-form-and-magnitude-practice","Three Dimensional Vector Operations - 3D Vector Operations Worksheet - Component Form and Magnitude Practice","","Kuta Software-Infinite Precalculus worksheet focused on three-dimensional vectors, requiring learners to find component forms of resultant vectors and compute the magnitude of those results. Problems provide vectors such as f, u, g and sets labeled A, B, C, D as well as products like AB, CD, TX, and YZ. It emphasizes applying vector operations consistently across multiple examples to practice both coordinate-based results and overall length.",{"@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-operations-3d-vector-operations-worksheet-component-form-and-magnitude-practice/523548/",{"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-operations-3d-vector-operations-worksheet-component-form-and-magnitude-practice/523548.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What skills does this worksheet practice for 3D vectors?","Question",{"text":112,"@type":113},"It practices finding the component form of resultant vectors and calculating the magnitude (length) of those resultant vectors.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are resultant vectors formed in the problems?",{"text":117,"@type":113},"Many items combine given vectors through operations like AB, CD, TX, YZ, or similar expressions, then ask for the resultant components.",{"name":119,"@type":110,"acceptedAnswer":120},"What does the “magnitude of the resultant vector” section require?",{"text":121,"@type":113},"It requires computing the length of the resultant vector formed from the specified vector operation(s), using the resultant’s components.","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},523548,1791753317,{"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":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"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":52,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Precalculus  \nThree Dimensional Vector Operations  \nName  Date  Period   \nFind the component form of the resultant vector.  \n1) f 􀀠 􀀐􀀙 , 􀀐􀀛 , 􀀛 2) u   􀀠 􀀓 , 􀀜 , 􀀐􀀗 g 􀀠 􀀛 , 􀀐 􀀘 , 􀀖  g 􀀠 􀀜 , 􀀚 , 􀀐􀀚 Find: f 􀀎 g Find: u 􀀐 g  \n3) Given: A = (􀀐􀀙 , 􀀐􀀖 , 􀀐􀀘 ) B = (􀀐􀀗 , 􀀐􀀛 , 􀀘 ) 4) Given: T = (􀀐􀀕 􀀗 􀀐􀀔) X = (􀀖 􀀐􀀕 􀀐􀀘 )  C = (􀀐􀀕 , 􀀖 , 􀀐􀀗) D = (􀀐􀀙 , 􀀘 , 􀀓) Y = (􀀚 , 􀀘, , 􀀐, 􀀔) Z = (􀀚 , 􀀖,, 􀀐 􀀗, )  \nFind: 􀀐AB 􀀐 CD Find: TX 􀀎 YZ  \n5) a 􀀠 􀀔 , 􀀐􀀛 , 􀀘 6) u 􀀠 􀀐􀀕 , 􀀘 , 􀀐􀀙 g 􀀠 􀀐􀀙 , 􀀚 , 􀀐􀀚 g 􀀠 􀀐􀀕 , 􀀐􀀖 , 􀀛 Find: 􀀐  a   􀀐 􀀗g  Find: 􀀗 u 􀀎 􀀔􀀓g   \n7) Given: A = (􀀐􀀙 , 􀀐􀀙 , 􀀐􀀗) B = (􀀗 , 􀀐􀀛 , 􀀚) 8) Given: P = (􀀓 􀀜 􀀚) Q = (􀀐􀀜 􀀐􀀗 􀀔)  C = (􀀛 , 􀀜 , 􀀘 ) D = (􀀚 , 􀀕 , 􀀐􀀜) R = (􀀜,, 􀀐,􀀜 , 􀀐􀀗) S = ( 􀀐, 􀀛 , 􀀕, , 􀀓)  \nFind: 􀀘AB 􀀎 􀀔􀀓 CD Find: 􀀙PQ 􀀐 􀀘RS  \nFind the magnitude of the resultant vector.  \n9) f 􀀠 􀀐􀀜 , 􀀔 , 􀀐􀀚 10) f 􀀠 􀀘 , 􀀔 , 􀀓 v 􀀠 􀀗 , 􀀐 􀀔 , 􀀓 v 􀀠 􀀖 , 􀀚 , 􀀚 Find: f 􀀎 v Find: 􀀐 f 􀀎 v  \n11) Given: A = (􀀐􀀕 , 􀀖 , 􀀖) B = (􀀗 , 􀀐􀀜 , 􀀓) 12) Given: P = (􀀐􀀚 , 􀀚 , 􀀐􀀚 ) Q = (􀀔 , 􀀐􀀛 , 􀀐􀀜)  C = (􀀘 , 􀀐􀀗 , 􀀕) D = (􀀛 , 􀀐􀀘 , 􀀔) R = (􀀐􀀚 , 􀀐􀀖 , 􀀘 ) S = (􀀐􀀖 , 􀀓 , 􀀓)  \nFind: AB 􀀐 CD Find: 􀀐PQ 􀀐 RS  \n13) u 􀀠 􀀐􀀙 , 􀀐􀀚 , 􀀔  14) u 􀀠 􀀐􀀗 , 􀀐􀀗 , 􀀜 g 􀀠 􀀐􀀕 , 􀀕 , 􀀐􀀛 g 􀀠 􀀐􀀛 , 􀀗 , 􀀗 Find: 􀀐􀀖 u   􀀐 􀀔􀀓g    Find: 􀀕 u   􀀎 􀀘 g    \n15) Given: A = (􀀛 , 􀀐􀀖 , 􀀜) B = (􀀐􀀘 , 􀀔 , 􀀙) 16) Given: T = (􀀐􀀖 􀀐􀀚 􀀐􀀙) X = (􀀖 􀀙 􀀐􀀔)  C = (􀀐􀀗 , 􀀐􀀜 , 􀀘 ) D = (􀀐􀀛 , 􀀛 , 􀀐􀀕)  Y = (􀀐􀀜 ,, 􀀐 􀀗 ,, 􀀐􀀜) Z = (􀀘 ,, 􀀔 ,, 􀀐􀀕)  \nFind: 􀀐AB 􀀎 CD Find: 􀀙 TX 􀀎 􀀚YZ  \nKuta Software-Infinite Precalculus  \nThree Dimensional Vector Operations  \nFind the component form of the resultant vector.  \n1) f 􀀠 􀀐􀀙 , 􀀐􀀛 , 􀀛 g 􀀠 􀀛 , 􀀐 􀀘 , 􀀖  Find: f 􀀎 g  \n􀀕 , 􀀐􀀔􀀖 , 􀀔􀀔   \n3) Given: A = (􀀐􀀙 , 􀀐􀀖 , 􀀐􀀘 ) B = (􀀐􀀗 , 􀀐􀀛 , 􀀘 )  \n C = (􀀐􀀕 , 􀀖 , 􀀐􀀗) D = (􀀐􀀙 , 􀀘 , 􀀓) Find: 􀀐AB 􀀐 CD  \n􀀕 , 􀀖 , 􀀐􀀔􀀗  \n5) a 􀀠 􀀔 , 􀀐􀀛 , 􀀘 g 􀀠 􀀐􀀙 , 􀀚 , 􀀐􀀚 Find: 􀀐  a   􀀐 􀀗g  \n􀀕􀀖 , 􀀐􀀕􀀓 , 􀀕􀀖  \n7) Given: A = (􀀐􀀙 , 􀀐􀀙 , 􀀐􀀗) B = (􀀗 , 􀀐􀀛 , 􀀚)  \n C = (􀀛 , 􀀜 , 􀀘 ) D = (􀀚 , 􀀕 , 􀀐􀀜) Find: 􀀘AB 􀀎 􀀔􀀓 CD  \n􀀗􀀓 , 􀀐􀀛􀀓 , 􀀐􀀛􀀘  \nName  Date  Period   \n2) u 􀀠 􀀓 , 􀀜 , 􀀐􀀗 g 􀀠 􀀜 , 􀀚 , 􀀐􀀚 Find: u 􀀐 g  \n􀀐􀀜 , 􀀕 , 􀀖  \n4) Given: T = (􀀐􀀕 , 􀀗 , 􀀐􀀔) X = (􀀖 , 􀀐􀀕 , 􀀐􀀘 )  \n Y = (􀀚 , 􀀘 , 􀀐􀀔) Z = (􀀚 , 􀀖 , 􀀐􀀗) Find: TX 􀀎 YZ  \n􀀘 , 􀀐􀀛 , 􀀐􀀚  \n6) u 􀀠 􀀐􀀕 , 􀀘 , 􀀐􀀙 g 􀀠 􀀐􀀕 , 􀀐􀀖 , 􀀛 Find: 􀀗 u 􀀎 􀀔􀀓g   \n􀀐􀀕􀀛 , 􀀐􀀔􀀓 , 􀀘􀀙  \n8) Given: P = (􀀓 , 􀀜 , 􀀚) Q = (􀀐􀀜 , 􀀐􀀗 , 􀀔)  \n R = (􀀜 , 􀀐􀀜 , 􀀐􀀗) S = (􀀐􀀛 , 􀀕 , 􀀓) Find: 􀀙PQ 􀀐 􀀘RS  \n􀀖􀀔 , 􀀐􀀔􀀖􀀖 , 􀀐􀀘􀀙  \nFind the magnitude of the resultant vector.  \n9) f 􀀠 􀀐􀀜 , 􀀔 , 􀀐􀀚 v 􀀠 􀀗 , 􀀐 􀀔 , 􀀓 Find: f 􀀎 v  \n􀀚􀀗 􀁼 􀀛􀀑􀀙􀀓􀀕  \n11) Given: A = (􀀐􀀕 , 􀀖 , 􀀖) B = (􀀗 , 􀀐􀀜 , 􀀓)  \n C = (􀀘 , 􀀐􀀗 , 􀀕) D = (􀀛 , 􀀐􀀘 , 􀀔) Find: AB 􀀐 CD  \n􀀔􀀖􀀗 􀁼 􀀔􀀔􀀑􀀘􀀚􀀙  \n13) u 􀀠 􀀐􀀙 , 􀀐􀀚 , 􀀔  g 􀀠 􀀐􀀕 , 􀀕 , 􀀐􀀛 Find: 􀀐􀀖 u   􀀐 􀀔􀀓g    \n􀀚􀀖􀀚􀀗 􀁼 􀀛􀀘􀀑􀀛􀀚􀀕  \n15) Given: A = (􀀛 , 􀀐􀀖 , 􀀜) B = (􀀐􀀘 , 􀀔 , 􀀙)  \n C = (􀀐􀀗 , 􀀐􀀜 , 􀀘 ) D = (􀀐􀀛 , 􀀛 , 􀀐􀀕) Find: 􀀐AB 􀀎 CD  \n􀀕􀀙􀀙 􀁼 􀀔􀀙􀀑􀀖􀀔  \n10) f 􀀠 􀀘 , 􀀔 , 􀀓 v 􀀠 􀀖 , 􀀚 , 􀀚 Find: 􀀐 f 􀀎 v  \n􀀛􀀜 􀁼 􀀜􀀑􀀗􀀖􀀗  \n12) Given: P = (􀀐􀀚 , 􀀚 , 􀀐􀀚 ) Q = (􀀔 , 􀀐􀀛 , 􀀐􀀜)  \n R = (􀀐􀀚 , 􀀐􀀖 , 􀀘 ) S = (􀀐􀀖 , 􀀓 , 􀀓) Find: 􀀐PQ 􀀐 RS  \n􀀖􀀖􀀚 􀁼 􀀔􀀛􀀑􀀖􀀘􀀛  \n14) u 􀀠 􀀐􀀗 , 􀀐􀀗 , 􀀜 g 􀀠 􀀐􀀛 , 􀀗 , 􀀗 Find: 􀀕 u   􀀎 􀀘 g    \n􀀕 􀀜􀀚􀀖 􀁼 􀀙􀀕􀀑􀀖􀀛􀀙  \n16) Given: T = (􀀐􀀖 , 􀀐􀀚 , 􀀐􀀙) X = (􀀖 , 􀀙 , 􀀐􀀔)  Y = (􀀐􀀜 , 􀀐 􀀗 , 􀀐􀀜) Z = (􀀘 , 􀀔 , 􀀐􀀕)  \nFind: 􀀙 TX 􀀎 􀀚YZ  \n􀀖􀀙􀀜􀀙􀀙 􀁼 􀀔􀀜􀀕􀀑􀀕􀀙􀀘  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaivzKb8s4h94p","https://ap.wps.com/l/cbCaivzKb8s4h94p","pdf",37974,"English","# Find the component form of the resultant vector\n## Vector sums and products (AB, CD, TX, YZ)\n# Find the magnitude of the resultant vector\n## Vector magnitude calculations","[{\"question\":\"What skills does this worksheet practice for 3D vectors?\",\"answer\":\"It practices finding the component form of resultant vectors and calculating the magnitude (length) of those resultant vectors.\"},{\"question\":\"How are resultant vectors formed in the problems?\",\"answer\":\"Many items combine given vectors through operations like AB, CD, TX, YZ, or similar expressions, then ask for the resultant components.\"},{\"question\":\"What does the “magnitude of the resultant vector” section require?\",\"answer\":\"It requires computing the length of the resultant vector formed from the specified vector operation(s), using the resultant’s components.\"}]","Three Dimensional Vector Operations - 3D Vector Operations Worksheet - Component Form and Magnitude Practice | PDF",1791426991]