{"id":20261,"date":"2024-04-15T05:50:32","date_gmt":"2024-04-15T05:50:32","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20261"},"modified":"2024-04-15T05:50:32","modified_gmt":"2024-04-15T05:50:32","slug":"curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/","title":{"rendered":"Curl of vector \\[\\overrightarrow {\\rm{F}} = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} – 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}\\] is A. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] B. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} – 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] C. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} – 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\] D. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]"},"content":{"rendered":"

[amp_mcq option1=”\\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\]” option2=”\\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} – 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\]” option3=”\\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} – 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]” option4=”\\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]” correct=”option4″]<\/p>\n

The correct answer is $\\boxed{\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}}$.<\/p>\n

The curl of a vector field $\\overrightarrow F$ is defined as<\/p>\n

$$\\nabla \\times \\overrightarrow F = \\left( \\dfrac{\\partial Q}{\\partial x} – \\dfrac{\\partial P}{\\partial z} \\right){\\rm{\\hat i}} + \\left( \\dfrac{\\partial R}{\\partial y} – \\dfrac{\\partial Q}{\\partial z} \\right){\\rm{\\hat j}} + \\left( \\dfrac{\\partial P}{\\partial y} – \\dfrac{\\partial R}{\\partial x} \\right){\\rm{\\hat k}}$$<\/p>\n

where $P$, $Q$, and $R$ are the $x$, $y$, and $z$ components of $\\overrightarrow F$, respectively.<\/p>\n

In this case, $\\overrightarrow F = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} – 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}$. Therefore,<\/p>\n

$$P = {{\\rm{x}}^2}{{\\rm{z}}^2}, \\quad Q = -2{\\rm{x}}{{\\rm{y}}^2}, \\quad R = 2{{\\rm{y}}^2}{{\\rm{z}}^3}$$<\/p>\n

Substituting these values into the formula for the curl, we get<\/p>\n

$$\\nabla \\times \\overrightarrow F = \\left( \\dfrac{\\partial}{\\partial x} \\left( 2{{\\rm{y}}^2}{{\\rm{z}}^3} \\right) – \\dfrac{\\partial}{\\partial z} \\left( {{\\rm{x}}^2}{{\\rm{z}}^2} \\right) \\right){\\rm{\\hat i}} + \\left( \\dfrac{\\partial}{\\partial y} \\left( -2{\\rm{x}}{{\\rm{y}}^2} \\right) – \\dfrac{\\partial}{\\partial z} \\left( 2{{\\rm{y}}^2}{{\\rm{z}}^3} \\right) \\right){\\rm{\\hat j}} + \\left( \\dfrac{\\partial}{\\partial y} \\left( {{\\rm{x}}^2}{{\\rm{z}}^2} \\right) – \\dfrac{\\partial}{\\partial x} \\left( -2{\\rm{x}}{{\\rm{y}}^2} \\right) \\right){\\rm{\\hat k}}$$<\/p>\n

$$= \\left( 6{{\\rm{y}}^2}{{\\rm{z}}^2} – 2{{\\rm{x}}^2}{{\\rm{z}}^3} \\right){\\rm{\\hat i}} + \\left( -4{\\rm{x}}{{\\rm{y}}^3} – 2{{\\rm{y}}^2}{{\\rm{z}}^3} \\right){\\rm{\\hat j}} + \\left( 2{{\\rm{x}}^2}{{\\rm{z}}^2} + 4{\\rm{x}}{{\\rm{y}}^2} \\right){\\rm{\\hat k}}$$<\/p>\n

$$= \\left( 4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}$$<\/p>\n

Therefore, the curl of $\\overrightarrow F$ is $\\boxed{\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}}$.<\/p>\n","protected":false},"excerpt":{"rendered":"

[amp_mcq option1=”\\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\]” option2=”\\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} – 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\]” option3=”\\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} – 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]” option4=”\\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]” correct=”option4″]<\/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":[],"class_list":["post-20261","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\nCurl of vector \\[\\overrightarrow {\\rm{F}} = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} - 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}\\] is A. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] B. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} - 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] C. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} - 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\] D. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]<\/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\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Curl of vector \\[\\overrightarrow {\\rm{F}} = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} - 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}\\] is A. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] B. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} - 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] C. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} - 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\] D. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=”[left( {4{rm{y}}{{rm{z}}^3} + 2{rm{x}}{{rm{y}}^2}} right){rm{hat i}} + 2{{rm{x}}^2}{rm{zhat j}} – 2{{rm{y}}^2}{rm{zhat k}}]” option2=”[left( {4{rm{y}}{{rm{z}}^3} + 2{rm{x}}{{rm{y}}^2}} right){rm{hat i}} – 2{{rm{x}}^2}{rm{zhat j}} – 2{{rm{y}}^2}{rm{zhat k}}]” option3=”[2{rm{x}}{{rm{z}}^2}{rm{hat i}} – 4{rm{xyzhat j}} + 6{{rm{y}}^2}{{rm{z}}^2}{rm{hat k}}]” option4=”[2{rm{x}}{{rm{z}}^2}{rm{hat i}} + 4{rm{xyzhat j}} + 6{{rm{y}}^2}{{rm{z}}^2}{rm{hat k}}]” correct=”option4″]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:50:32+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Curl of vector \\[\\overrightarrow {\\rm{F}} = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} - 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}\\] is A. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] B. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} - 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] C. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} - 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\] D. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]","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\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/","og_locale":"en_US","og_type":"article","og_title":"Curl of vector \\[\\overrightarrow {\\rm{F}} = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} - 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}\\] is A. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] B. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} - 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] C. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} - 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\] D. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]","og_description":"[amp_mcq option1=”[left( {4{rm{y}}{{rm{z}}^3} + 2{rm{x}}{{rm{y}}^2}} right){rm{hat i}} + 2{{rm{x}}^2}{rm{zhat j}} – 2{{rm{y}}^2}{rm{zhat k}}]” option2=”[left( {4{rm{y}}{{rm{z}}^3} + 2{rm{x}}{{rm{y}}^2}} right){rm{hat i}} – 2{{rm{x}}^2}{rm{zhat j}} – 2{{rm{y}}^2}{rm{zhat k}}]” option3=”[2{rm{x}}{{rm{z}}^2}{rm{hat i}} – 4{rm{xyzhat j}} + 6{{rm{y}}^2}{{rm{z}}^2}{rm{hat k}}]” option4=”[2{rm{x}}{{rm{z}}^2}{rm{hat i}} + 4{rm{xyzhat j}} + 6{{rm{y}}^2}{{rm{z}}^2}{rm{hat k}}]” correct=”option4″]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:50:32+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/","url":"https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/","name":"Curl of vector \\[\\overrightarrow {\\rm{F}} = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} - 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}\\] is A. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] B. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} - 2{{\\rm{x}}^2}{\\rm{z\\hat j}} - 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] C. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} - 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\] D. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-04-15T05:50:32+00:00","dateModified":"2024-04-15T05:50:32+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/curl-of-vector-overrightarrow-rmf-rmx2rmz2rmhat-i-2rmxrmy2rmzhat-j-2rmy2rmz3rmhat-k-is-a-left-4\/#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":"Curl of vector \\[\\overrightarrow {\\rm{F}} = {{\\rm{x}}^2}{{\\rm{z}}^2}{\\rm{\\hat i}} – 2{\\rm{x}}{{\\rm{y}}^2}{\\rm{z\\hat j}} + 2{{\\rm{y}}^2}{{\\rm{z}}^3}{\\rm{\\hat k}}\\] is A. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} + 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] B. \\[\\left( {4{\\rm{y}}{{\\rm{z}}^3} + 2{\\rm{x}}{{\\rm{y}}^2}} \\right){\\rm{\\hat i}} – 2{{\\rm{x}}^2}{\\rm{z\\hat j}} – 2{{\\rm{y}}^2}{\\rm{z\\hat k}}\\] C. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} – 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\] D. \\[2{\\rm{x}}{{\\rm{z}}^2}{\\rm{\\hat i}} + 4{\\rm{xyz\\hat j}} + 6{{\\rm{y}}^2}{{\\rm{z}}^2}{\\rm{\\hat k}}\\]"}]},{"@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\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?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\/20261","targetHints":{"allow":["GET"]}}],"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=20261"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/20261\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=20261"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=20261"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=20261"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}