{"id":2036,"date":"2021-12-23T16:20:12","date_gmt":"2021-12-23T10:50:12","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2036"},"modified":"2023-12-26T13:40:29","modified_gmt":"2023-12-26T08:10:29","slug":"ncert-solutions-for-class-12-maths-chapter-10-vector-algebra-ex-10-3-exercise-10-3","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-3\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra (Ex 10.3) Exercise 10.3"},"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-10-3\/#NCERT_Solutions_for_Class_12_Maths_Chapter_10_Vector_Algebra_Exercise_103\" title=\"NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3\">NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3<\/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-10-3\/#FAQs_on_NCERT_Solutions_for_Class_12_Maths_Chapter_10_Vector_Algebra_Exercise_103\" title=\"FAQs on NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3\">FAQs on NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3<\/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-10-3\/#What_is_the_main_concept_given_in_this_Exercise\" title=\"What is the main concept given in this Exercise? \">What is the main concept given in this Exercise? <\/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-10-3\/#Which_is_the_most_important_question_from_this_Exercise\" title=\"Which is the most important question from this Exercise? \">Which is the most important question from this Exercise? <\/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-10-3\/#What_is_the_dot_product_of_2_Vectors\" title=\"What is the dot product of 2 Vectors? \">What is the dot product of 2 Vectors? <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>All the exercise questions in Chapter 10 of <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\"><strong>NCERT Solutions for Class 12 Maths<\/strong><\/a>, which covers Vector Algebra, have been thoroughly addressed. The concepts studied in Chapter 10 lay the groundwork for solving the exercises in <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/\"><strong>NCERT solutions for Class 12<\/strong><\/a> Exercise 10.3. This practice is essential for success in both the CBSE Term I exam and various competitive examinations. To prepare effectively for your exams, you can easily access and work on these NCERT Solutions by downloading them 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? 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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\/2036\" 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-10.3.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-10.3.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 10.3<br\/><\/a>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_10_Vector_Algebra_Exercise_103\"><\/span>NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Utilizing <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT solutions<\/strong><\/a> for Exercise 10.3 in Class 12 Maths proves to be the most advantageous approach for CBSE students gearing up for their examinations. This chapter encompasses a multitude of exercises, and one of them is Exercise 10.3, whose solutions are conveniently accessible in PDF format on this webpage. These solutions are also readily downloadable from our website or app. The dedicated subject matter experts at Infinite Learn have meticulously crafted these solutions, aligning them with CBSE guidelines.<\/p>\n<p>For Class 12 students who diligently complete all the exercises within this chapter, achieving high scores in exams becomes an attainable goal. By employing these solutions, students gain insights into the question patterns prevalent in this chapter&#8217;s examinations, as well as an understanding of the chapter&#8217;s marks allocation. This knowledge enables them to prepare effectively.<\/p>\n<p>Furthermore, this chapter boasts numerous additional exercises containing an extensive array of questions, all expertly designed by subject matter specialists. Consequently, these solutions are deemed of superior quality, and it is imperative for students to reference them. To excel in the exams, it is imperative to practice these solutions diligently, alongside solving all the accompanying questions.<\/p>\n<p>There is no need for procrastination. Waste no time and procure the NCERT solutions for Class 12 Maths Chapter 10 Exercise 10.3 from the Infinity Learn website immediately to enhance your exam readiness. If you possess the Infinite Learn app on your mobile device, we recommend downloading the solutions through the app for added convenience. These solutions can be utilized both online and offline, catering to your preferences.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_NCERT_Solutions_for_Class_12_Maths_Chapter_10_Vector_Algebra_Exercise_103\"><\/span>FAQs on NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\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><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-4\" target=\"_blank\" rel=\"noopener\"><strong>Exercise 10.4 Solutions 12<\/strong><\/a><\/li>\n<li><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-miscellaneous\" target=\"_blank\" rel=\"noopener\">Miscellaneous Exercise Chapter 10 Solutions<\/a><\/strong><\/li>\n<\/ul>\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=\"What_is_the_main_concept_given_in_this_Exercise\"><\/span>What is the main concept given in this Exercise? <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\tIt basically deals with the scalar product of two vectors. It actually define the dot product as the product of the magnitudes of the two vectors and the angle between the two vectors' cosine values. Another definition includes the product of a first-to-second projection and magnitude of the second vector. This exercise includes different problems related to the dot product of 2 vectors. \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_is_the_most_important_question_from_this_Exercise\"><\/span>Which is the most important question from this Exercise? <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 enhance 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 Exercise 10.3 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_is_the_dot_product_of_2_Vectors\"><\/span>What is the dot product of 2 Vectors? <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\tThis number (Scalar quantity) is generated by executing an operation on the vector components and it is termed the dot product or scalar product. Only vectors with the same number of dimensions can be merged using the dot product. The dot product has a heavy dot as its logo. It is a very important topic and must be learned well as it has multiple applications in some fields of Math and Physics. \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\": \"What is the main concept given in this Exercise? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"It basically deals with the scalar product of two vectors. It actually define the dot product as the product of the magnitudes of the two vectors and the angle between the two vectors' cosine values. Another definition includes the product of a first-to-second projection and magnitude of the second vector. This exercise includes different problems related to the dot product of 2 vectors.\"\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 is the most important question from this Exercise? \",\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 enhance 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 Exercise 10.3 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 is the dot product of 2 Vectors? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"This number (Scalar quantity) is generated by executing an operation on the vector components and it is termed the dot product or scalar product. Only vectors with the same number of dimensions can be merged using the dot product. The dot product has a heavy dot as its logo. It is a very important topic and must be learned well as it has multiple applications in some fields of Math and Physics.\"\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>All the exercise questions in Chapter 10 of NCERT Solutions for Class 12 Maths, which covers Vector Algebra, have been [&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":"exercise 10.3 class 12 maths","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3","_yoast_wpseo_metadesc":"Easy solutions for Class 12 Maths, Chapter 10 on Vector Algebra, Exercise 10.3, to help students learn and solve problems.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-3\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3<\/title>\n<meta name=\"description\" content=\"Easy solutions for Class 12 Maths, Chapter 10 on Vector Algebra, Exercise 10.3, to help students learn and solve problems.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-10-vector-algebra-exercise-10-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for 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