<[ 2 ], [ 0 ]><\/p>\n\n\n\n
To rotate a vector in a two-dimensional Cartesian plane, one can use the standard rotation formulas. These formulas describe how the coordinates of a point (x, y) change when rotated counter-clockwise by an angle \u03b8 about the origin to a new point (x’, y’). The transformation is given by:<\/p>\n\n\n\n
x’ = x cos(\u03b8) – y sin(\u03b8)
y’ = x sin(\u03b8) + y cos(\u03b8)<\/p>\n\n\n\n
In this problem, the initial vector is (0, 2), so its coordinates are x = 0 and y = 2. The angle of rotation is \u03b8 = 270\u00b0 counter-clockwise.<\/p>\n\n\n\n
The first step is to determine the values of the trigonometric functions for the angle of 270\u00b0. On the unit circle, an angle of 270\u00b0 corresponds to the point (0, -1). Therefore, the cosine of 270\u00b0 is the x-coordinate, and the sine of 270\u00b0 is the y-coordinate:<\/p>\n\n\n\n
cos(270\u00b0) = 0
sin(270\u00b0) = -1<\/p>\n\n\n\n
Now, these values can be substituted into the rotation formulas along with the coordinates of the original vector.<\/p>\n\n\n\n
For the new x-coordinate, x’:
x’ = (0) * cos(270\u00b0) – (2) * sin(270\u00b0)
x’ = (0)(0) – (2)(-1)
x’ = 0 – (-2)
x’ = 2<\/p>\n\n\n\n
For the new y-coordinate, y’:
y’ = (0) * sin(270\u00b0) + (2) * cos(270\u00b0)
y’ = (0)(-1) + (2)(0)
y’ = 0 + 0
y’ = 0<\/p>\n\n\n\n
Thus, the coordinates of the rotated vector are (2, 0).<\/p>\n\n\n\n
Geometrically, the original vector (0, 2) points directly upwards along the positive y-axis. A 90\u00b0 counter-clockwise rotation would place it on the negative x-axis at (-2, 0). A 180\u00b0 rotation would place it on the negative y-axis at (0, -2). Finally, a 270\u00b0 counter-clockwise rotation moves it to the positive x-axis. Since the rotation preserves the vector’s magnitude (length), which is 2, the final position must be (2, 0). This confirms the result obtained from the formulas.<\/p>\n\n\n\n Rotate the vector (0,2) 270\u00b0 counter-clockwise about the origin. <[ ? ], [ ]> The Correct Answer and Explanation is: <[ 2 ], [ 0 ]> To rotate a vector in a two-dimensional Cartesian plane, one can use the standard rotation formulas. These formulas describe how the coordinates of a point (x, y) change when […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-231401","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231401","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=231401"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231401\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-893.jpeg\")
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