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Exercises require drawing diagrams showing horizontal and vertical components, then finding each component’s magnitude, followed by overall vector magnitude and direction angles. Additional tasks ask for component form, magnitude, and direction angle for specified vectors, including sketching graphs to confirm magnitude and angle. A critical thinking item constructs a vector with a given magnitude in the opposite direction of another.",{"@graph":69,"@context":118},[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/two-dimensional-vector-basics-vector-component-forms-magnitudes-and-direction-angles/523544/",{"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/two-dimensional-vector-basics-vector-component-forms-magnitudes-and-direction-angles/523544.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":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114],{"name":109,"@type":110,"acceptedAnswer":111},"How is the direction angle obtained?","Question",{"text":112,"@type":113},"Some questions require also sketching a graph of the vector before calculating magnitude and direction angle to visualize the result.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does the critical thinking question ask you to construct?",{"text":117,"@type":113},"It asks for the component form of a vector v with magnitude 50 that points in the opposite direction of a given vector u.","https://schema.org",{"og:url":83,"og:type":120,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":122,"canonical":83},"index,follow",{"doc_id":124,"site_id":62},523544,1791731580,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":92,"user_avatar":129,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":135,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":67,"update_tm":139,"read_time":140,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Precalculus  \nTwo-Dimensional Vector Basics  \nName  Date  Period   \nWrite each vector in component form.  \n1) RS  where R = (􀀐􀀖 , 􀀜) S = (􀀛 , 􀀐􀀔) 2) PQ  where P = (􀀐􀀔􀀓 , 􀀘 ) Q = (􀀐􀀜 , 􀀐􀀔􀀓)  \n3)  \n4)  k  􀀠 􀀘􀀕 , 􀀔􀀚􀀗°  \nDraw a diagram to illustrate the horizontal and vertical components of the vector. Then find the magnitude of each component.  \n5)  t   􀀠 􀀕􀀙 , 􀀔􀀔􀀘° 6)  a  􀀠 􀀔􀀘 , 􀀕􀀖􀀓°  \nFind the magnitude and direction angle for each vector.  \n7) 􀀛 i  􀀎 􀀔􀀘j 8) r 􀀠 􀀐􀀛 , 􀀐􀀗􀀔   \nFind the component form, magnitude, and direction angle for the given vector  \n9) CD where C = (􀀙 , 􀀐􀀖) D = (􀀐􀀙 , 􀀐􀀜)  \nSketch a graph of each vector then find the magnitude and direction angle.  \n10) 􀀘 i~~ ~~ 􀀐 􀀔􀀕j 11) RS where R = (􀀐􀀜 , 􀀐􀀔) S = (􀀐􀀚 , 􀀐􀀖)  \nCritical thinking question:  \n12) Find the component form of v with a magnitude of 50 in the opposite direction of u 􀀠 􀀕 , 􀀐  \n 􀀖   \n􀀕  \nKuta Software-Infinite Precalculus  \nTwo-Dimensional Vector Basics  \nWrite each vector in component form.  \n1) RS  where R = (􀀐􀀖 , 􀀜) S = (􀀛 , 􀀐􀀔)  \n􀀔􀀔 , 􀀐􀀔􀀓  \n3)  \nName  Date  Period   \n2) PQ  where P = (􀀐􀀔􀀓 , 􀀘 ) Q = (􀀐􀀜 , 􀀐􀀔􀀓)  \n 􀀔 , 􀀐􀀔􀀘  \n4)  k  􀀠 􀀘􀀕 , 􀀔􀀚􀀗°  \n􀀐􀀘􀀔􀀑􀀚􀀕 , 􀀘􀀑􀀗􀀗  \nDraw a diagram to illustrate the horizontal and vertical components of the vector. Then find the  \nmagnitude of each component.  \n5)  t  \n􀀠 􀀕􀀙 , 􀀔􀀔􀀘°  \nx  \nHorizontal: 􀀐􀀔􀀓􀀑􀀜􀀜  \nVertical: 􀀕􀀖􀀑􀀘􀀙  \nFind the magnitude and direction angle for each vector.  \n7) 􀀛 i  􀀎 􀀔􀀘j   \n􀀔􀀚􀀙􀀔􀀑􀀜􀀖 °  \n8) r 􀀠 􀀐􀀛 , 􀀐􀀗􀀔   \n􀀔􀀚􀀗􀀘 􀁼 􀀗􀀔􀀑􀀚􀀚􀀖􀀕􀀘􀀛􀀑􀀜􀀙°  \nFind the component form, magnitude, and direction angle for the given vector  \n9) CD where C = (􀀙 , 􀀐􀀖) D = (􀀐􀀙 , 􀀐􀀜)  \n􀀐􀀔􀀕 , 􀀐􀀙  \n􀀙 􀀘 􀁼 􀀔􀀖􀀑􀀗􀀔􀀙  \n􀀕􀀓􀀙􀀑􀀘􀀚°  \nSketch a graph of each vector then find the magnitude and direction angle.  \nCritical thinking question:  \n12) Find the component form of v with a magnitude of 50 in the opposite direction of u 􀀠 􀀕 , 􀀐  \nv 􀀠 􀀐􀀗􀀓 , 􀀖􀀓  \n 􀀖   \n􀀕  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCainvbx3CFGd0Y","https://ap.wps.com/l/cbCainvbx3CFGd0Y","pdf",42351,"English","# Two-Dimensional Vector Basics\n## Write vectors in component form\n## Horizontal/vertical components and magnitudes\n## Magnitude and direction angle\n## Component form, magnitude, and direction angle\n## Sketch graphs and find magnitude/direction\n## Critical thinking problem","[{\"question\":\"How is the direction angle obtained?\",\"answer\":\"Some questions require also sketching a graph of the vector before calculating magnitude and direction angle to visualize the result.\"},{\"question\":\"What does the critical thinking question ask you to construct?\",\"answer\":\"It asks for the component form of a vector v with magnitude 50 that points in the opposite direction of a given vector u.\"}]","Two-Dimensional Vector Basics - Vector Component Forms, Magnitudes, and Direction Angles | PDF",1791426983,15]