{"id":2042,"date":"2021-12-23T16:21:36","date_gmt":"2021-12-23T10:51:36","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2042"},"modified":"2023-12-26T13:40:34","modified_gmt":"2023-12-26T08:10:34","slug":"ncert-solutions-for-class-12-maths-chapter-10-vector-algebra-miscellaneous-exercise","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\/#NCERT_Solutions_for_Class_12_Maths_Chapter_10_Vector_Algebra_Exercise_Miscellaneous\" title=\"NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise Miscellaneous\">NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise Miscellaneous<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\/#FAQs_on_NCERT_Solutions_for_Class_12_Maths_Chapter_10_Exercise_Miscellaneous\" title=\"FAQs on NCERT Solutions for Class 12 Maths Chapter 10 Exercise Miscellaneous\">FAQs on NCERT Solutions for Class 12 Maths Chapter 10 Exercise Miscellaneous<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\/#How_can_I_download_the_PDF_file_for_the_NCERT_Solutions_for_Exercise_Miscellaneous_of_this_Chapter\" title=\"How can I download the PDF file for the NCERT Solutions for Exercise Miscellaneous of this Chapter? \">How can I download the PDF file for the NCERT Solutions for Exercise Miscellaneous of this Chapter? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\/#Which_question_is_important_from_Exercise_Miscellaneous_of_this_Chapter\" title=\"Which question is important from Exercise Miscellaneous of this Chapter? \">Which question is important from Exercise Miscellaneous of this Chapter? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\/#What_types_of_questions_are_generally_asked_from_Exercise_Miscellaneous_of_this_Chapter\" title=\"What types of questions are generally asked from Exercise Miscellaneous of this Chapter? \">What types of questions are generally asked from Exercise Miscellaneous of this Chapter? <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>In <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT Solutions for Class 12<\/strong><\/a> Maths Chapter 10 on Vector Algebra, you will find answers to all miscellaneous exercise questions. The concepts covered in Chapter 10 serve as the building blocks for solving miscellaneous exercises in Class 12. This practice is vital not only for the CBSE Term I exam but also for various competitive exams. To boost your exam performance, you can easily access and download these NCERT Solutions for offline practice.<\/p>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? Are you preparing for Exams?<\/span>\n\t\t\t<span class=\"subtitle\">Study without Internet (Offline)<\/span>\n\t\t\t\n\t\t\t<button class=\"download-pdf-btn\" type=\"submit\"><img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/themes\/blog\/assets\/download-icon.svg\" alt=\"Download PDF icon\" width=\"18px\" height=\"18px\">Download PDF<\/button>\n\t\t<\/div>\n\t\t<div class=\"custom-model-main pdf-download-modal\">\n\t\t\t<div class=\"custom-model-inner\">\n\t\t\t\t<div class=\"close-modal-btn close-pdf-btn\">\u00d7<\/div>\n\t\t\t\t<div class=\"custom-model-wrap\">\n\t\t\t\t\t<div class=\"pop-up-content-wrap\">\n\t\t\t\t\t<div role=\"form\" class=\"wpcf7\" id=\"wpcf7-f314520-o1\" lang=\"en-US\" dir=\"ltr\">\n<div class=\"screen-reader-response\"><p role=\"status\" aria-live=\"polite\" aria-atomic=\"true\"><\/p> <ul><\/ul><\/div>\n<form action=\"\/surge\/wp-json\/wp\/v2\/posts\/2042#wpcf7-f314520-o1\" method=\"post\" class=\"wpcf7-form init\" novalidate=\"novalidate\" 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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/2042\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-10.-Miscellaneous.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-10.-Miscellaneous.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Exercise 10. Miscellaneous<br\/><\/a>\n<h2 aria-level=\"2\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_10_Vector_Algebra_Exercise_Miscellaneous\"><\/span>NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Utilizing <strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\">NCERT solutions for Class 12 Maths<\/a><\/strong> Miscellaneous Exercises proves to be the optimal choice for CBSE students gearing up for their examinations. This particular chapter encompasses a variety of exercises, including the Miscellaneous Exercise, and you can readily access the corresponding solutions in PDF format on this webpage. Alternatively, you have the option to download these solutions from our website or app. Our team of Infinite Learn subject matter experts meticulously crafted these solutions, adhering to all CBSE guidelines.<\/p>\n<p>Students in Class 12 who diligently complete all the exercises in this chapter position themselves for success in their exams. By employing these solutions, students gain insight into the question patterns prevalent in this chapter&#8217;s examinations and discern the weightage of marks allocated to it, facilitating comprehensive preparation.<\/p>\n<p>Beyond the Miscellaneous Exercise, this chapter features numerous other exercises with an abundance of questions, each boasting solutions meticulously developed by our subject matter experts. Consequently, all of these solutions are recognized for their superior quality, making it imperative for students to incorporate them into their study regimen to achieve stellar results in their exams. We encourage students not to procrastinate any further and promptly download the <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT solutions<\/strong><\/a> for Class 12 Maths Chapter 10 Miscellaneous Exercise from the Infinity Learn website, or via the Infinite Learn app if it is installed on their mobile devices. These solutions are accessible both online and offline, ensuring flexibility in study resources.<\/p>\n<p><strong>Also Check:<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-1\" target=\"_blank\" rel=\"noopener\">Exercise 10.1 Solutions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-2\" target=\"_blank\" rel=\"noopener\">Exercise 10.2 Solutions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-3\" target=\"_blank\" rel=\"noopener\">Exercise 10.3 Solutions<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-4\" target=\"_blank\" rel=\"noopener\">Exercise 10.4 Solutions<\/a><\/strong><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_NCERT_Solutions_for_Class_12_Maths_Chapter_10_Exercise_Miscellaneous\"><\/span>FAQs on NCERT Solutions for Class 12 Maths Chapter 10 Exercise Miscellaneous<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_can_I_download_the_PDF_file_for_the_NCERT_Solutions_for_Exercise_Miscellaneous_of_this_Chapter\"><\/span>How can I download the PDF file for the NCERT Solutions for Exercise Miscellaneous of this Chapter? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe NCERT Solutions are easily available on the INFINITE learn site. Follow these steps to download them:  Visit the official page of Infinite learn.  The webpage with Infinite learn NCERT Solutions for Miscellaneous Exercise of Chapter 10 of Class 12 Maths will open.  To download this, click on the Download PDF button and you can view the NCERT Solutions offline. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Which_question_is_important_from_Exercise_Miscellaneous_of_this_Chapter\"><\/span>Which question is important from Exercise Miscellaneous of this Chapter? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn reality, there is no such essential question! You can notice, the easier questions help you recall the concept, while the difficult ones enhances your problem-solving abilities and how you can use your concepts in the problems for practice. That\u2019s why all the questions are necessary. For Miscellaneous Exercise of Chapter 10 of Class 12 Maths, you must be attentive. Students must solve all the questions difficult or easy.  \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_types_of_questions_are_generally_asked_from_Exercise_Miscellaneous_of_this_Chapter\"><\/span>What types of questions are generally asked from Exercise Miscellaneous of this Chapter? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tProbably, only questions having the marks weightage of four marks come from Miscellaneous Exercise of Chapter 10 of Class 12 Maths. If the student is sure about his abilities and how good can he grasp the related concepts, he can easily score good marks if any question is set from Miscellaneous Exercise of Chapter 10 of Class 12 Maths and do good in his exams. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How can I download the PDF file for the NCERT Solutions for Exercise Miscellaneous of this Chapter? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The NCERT Solutions are easily available on the INFINITE learn site. Follow these steps to download them:  Visit the official page of Infinite learn.  The webpage with Infinite learn NCERT Solutions for Miscellaneous Exercise of Chapter 10 of Class 12 Maths will open.  To download this, click on the Download PDF button and you can view the NCERT Solutions offline.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Which question is important from Exercise Miscellaneous of this Chapter? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In reality, there is no such essential question! You can notice, the easier questions help you recall the concept, while the difficult ones enhances your problem-solving abilities and how you can use your concepts in the problems for practice. That\u2019s why all the questions are necessary. For Miscellaneous Exercise of Chapter 10 of Class 12 Maths, you must be attentive. Students must solve all the questions difficult or easy.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What types of questions are generally asked from Exercise Miscellaneous of this Chapter? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Probably, only questions having the marks weightage of four marks come from Miscellaneous Exercise of Chapter 10 of Class 12 Maths. If the student is sure about his abilities and how good can he grasp the related concepts, he can easily score good marks if any question is set from Miscellaneous Exercise of Chapter 10 of Class 12 Maths and do good in his exams.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>In NCERT Solutions for Class 12 Maths Chapter 10 on Vector Algebra, you will find answers to all miscellaneous exercise [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Solutions for Class 12 Maths Chapter 10 Exercise Miscellaneous","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Chapter 10 Miscellaneous Exercise","_yoast_wpseo_metadesc":"Simple solutions for Class 12 Maths, Chapter 10 - Vector Algebra, covering every question in the Miscellaneous Exercise.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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