{"id":20223,"date":"2024-04-15T05:50:03","date_gmt":"2024-04-15T05:50:03","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20223"},"modified":"2024-04-15T05:50:03","modified_gmt":"2024-04-15T05:50:03","slug":"the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/","title":{"rendered":"The vector function \\[\\overrightarrow {\\text{A}} \\] is given by \\[\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}\\] where u(x, y) is a scalar function, Then \\[\\left| {\\overrightarrow \\nabla \\times \\overrightarrow {\\text{A}} } \\right|\\] A. -1 B. 0 C. 1 D. \\[\\infty \\]"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9a26bddf44b\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    &#8221;-1&#8243;                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    &#8221;0&#8243;                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    &#8221;1&#8243;                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    &#8221;[infty                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    &#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is $\\boxed{0}$.<\/p>\n<p>The gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and its magnitude is equal to the magnitude of the <div class=\"youtube-subscribe-container\">\r\n  <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div>       <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> greatest rate of increase of the scalar field.<\/p>\n<p>The curl of a vector field is a vector field that represents the circulation of the vector field around a small loop.<\/p>\n<p>The curl of the gradient of a scalar field is always zero. This is because the gradient points in the direction of the greatest rate of increase of the scalar field, and the curl measures the circulation of a vector field around a small loop. If the vector field is always pointing in the same direction, then there is no circulation around a small loop, and the curl is zero.<\/p>\n<p>In this case, the vector field $\\overrightarrow {\\text{A}}$ is given by $\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}$ where u(x, y) is a scalar function. This means that $\\overrightarrow {\\text{A}}$ is the gradient of the scalar field u(x, y). Therefore, the curl of $\\overrightarrow {\\text{A}}$ is zero.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8221; Join Our Telegram Channel Subscribe on YouTube correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The vector function \\[\\overrightarrow {\\text{A}} \\] is given by \\[\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}\\] where u(x, y) is a scalar function, Then \\[\\left| {\\overrightarrow \\nabla \\times \\overrightarrow {\\text{A}} } \\right|\\] A. -1 B. 0 C. 1 D. \\[\\infty \\]<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The vector function \\[\\overrightarrow {\\text{A}} \\] is given by \\[\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}\\] where u(x, y) is a scalar function, Then \\[\\left| {\\overrightarrow \\nabla \\times \\overrightarrow {\\text{A}} } \\right|\\] A. -1 B. 0 C. 1 D. \\[\\infty \\]\" \/>\n<meta property=\"og:description\" content=\"Join Our Telegram Channel Subscribe on YouTube &#8221; correct=&#8221;option1&#8243;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:50:03+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The vector function \\[\\overrightarrow {\\text{A}} \\] is given by \\[\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}\\] where u(x, y) is a scalar function, Then \\[\\left| {\\overrightarrow \\nabla \\times \\overrightarrow {\\text{A}} } \\right|\\] A. -1 B. 0 C. 1 D. \\[\\infty \\]","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/","og_locale":"en_US","og_type":"article","og_title":"The vector function \\[\\overrightarrow {\\text{A}} \\] is given by \\[\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}\\] where u(x, y) is a scalar function, Then \\[\\left| {\\overrightarrow \\nabla \\times \\overrightarrow {\\text{A}} } \\right|\\] A. -1 B. 0 C. 1 D. \\[\\infty \\]","og_description":"Join Our Telegram Channel Subscribe on YouTube &#8221; correct=&#8221;option1&#8243;]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:50:03+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/","name":"The vector function \\[\\overrightarrow {\\text{A}} \\] is given by \\[\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}\\] where u(x, y) is a scalar function, Then \\[\\left| {\\overrightarrow \\nabla \\times \\overrightarrow {\\text{A}} } \\right|\\] A. -1 B. 0 C. 1 D. \\[\\infty \\]","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T05:50:03+00:00","dateModified":"2024-04-15T05:50:03+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-vector-function-overrightarrow-texta-is-given-by-overrightarrow-texta-overrightarrow-nabla-textu-where-ux-y-is-a-scalar-function-then-left-ov\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Engineering maths","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/engineering-maths\/"},{"@type":"ListItem","position":4,"name":"Calculus","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/engineering-maths\/calculus\/"},{"@type":"ListItem","position":5,"name":"The vector function \\[\\overrightarrow {\\text{A}} \\] is given by \\[\\overrightarrow {\\text{A}} = \\overrightarrow \\nabla {\\text{u,}}\\] where u(x, y) is a scalar function, Then \\[\\left| {\\overrightarrow \\nabla \\times \\overrightarrow {\\text{A}} } \\right|\\] A. -1 B. 0 C. 1 D. \\[\\infty \\]"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/20223"}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=20223"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/20223\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=20223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=20223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=20223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}