{"id":34,"date":"2025-04-07T10:38:44","date_gmt":"2025-04-07T10:38:44","guid":{"rendered":"https:\/\/makpal.studyedu.kz\/?page_id=34"},"modified":"2025-05-13T05:38:18","modified_gmt":"2025-05-13T05:38:18","slug":"%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%b4%d1%8b%d2%a3-%d0%ba%d0%be%d0%be%d1%80%d0%b4%d0%b8%d0%bd%d0%b0%d1%82%d0%b0%d0%bb%d0%b0%d1%80%d1%8b","status":"publish","type":"page","link":"https:\/\/makpal.studyedu.kz\/?page_id=34","title":{"rendered":"\u0412\u0435\u043a\u0442\u043e\u0440\u0434\u044b\u04a3 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043b\u0430\u0440\u044b"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\"><strong>\u041c\u0430\u049b\u0441\u0430\u0442\u044b:<\/strong><\/h3>\n\n\n\n<p>\u041e\u049b\u0443\u0448\u044b\u043d\u044b \u043a\u0435\u04a3\u0456\u0441\u0442\u0456\u043a\u0442\u0435\u0433\u0456 \u0435\u043a\u0456 \u043d\u04af\u043a\u0442\u0435 \u0430\u0440\u049b\u044b\u043b\u044b \u0432\u0435\u043a\u0442\u043e\u0440 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043b\u0430\u0440\u044b\u043d \u0442\u0430\u0431\u0443\u0493\u0430 \u04af\u0439\u0440\u0435\u0442\u0443. \u0422\u0435\u043e\u0440\u0438\u044f\u043d\u044b \u0442\u0456\u0440\u0435\u043a \u0441\u044b\u0437\u0431\u0430 \u0436\u04d9\u043d\u0435 \u043c\u044b\u0441\u0430\u043b\u0434\u0430\u0440 \u0430\u0440\u049b\u044b\u043b\u044b \u0431\u0435\u043a\u0456\u0442\u0443.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"> <strong>\u049a\u044b\u0441\u049b\u0430\u0448\u0430 \u0442\u0435\u043e\u0440\u0438\u044f:<\/strong> <\/h3>\n\n\n\n<p>\u0412\u0435\u043a\u0442\u043e\u0440 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043b\u0430\u0440\u044b \u0434\u0435\u0433\u0435\u043d \u043d\u0435?<\/p>\n\n\n\n<p>\u041a\u0435\u04a3\u0456\u0441\u0442\u0456\u043a\u0442\u0435\u0433\u0456 \u0435\u043a\u0456 \u043d\u04af\u043a\u0442\u0435 A(x1,y1,z1)\u0436\u04d9\u043d\u0435 B(x2,y2,z2) \u0431\u0435\u0440\u0456\u043b\u0441\u0435,<br><strong>\u0432\u0435\u043a\u0442\u043e\u0440 <\/strong><strong>AB<\/strong><strong>\u20d7<\/strong><strong>\\vec{AB}<\/strong> \u043a\u0435\u043b\u0435\u0441\u0456\u0434\u0435\u0439 \u0442\u0430\u0431\u044b\u043b\u0430\u0434\u044b:<\/p>\n\n\n\n<p>AB\u20d7=(x2\u2212x1;\u2005\u200ay2\u2212y1;\u2005\u200az2\u2212z1)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u0412\u0435\u043a\u0442\u043e\u0440 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u0441\u044b\u043d\u044b\u04a3 \u0436\u0430\u043b\u043f\u044b \u0431\u0435\u043b\u0433\u0456\u043b\u0435\u043d\u0443\u0456:<\/h4>\n\n\n\n<p>\u0412\u0435\u043a\u0442\u043e\u0440 a\u20d7=(ax,ay,az)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u0422\u0456\u0440\u0435\u043a \u0441\u044b\u0437\u0431\u0430 (\u0431\u043b\u043e\u043a-\u0441\u0445\u0435\u043c\u0430):<\/strong><\/h3>\n\n\n\n<p>\u0411\u04b1\u043b \u0442\u0456\u0440\u0435\u043a \u0441\u044b\u0437\u0431\u0430\u043d\u044b \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u0442\u0456 \u0442\u04af\u0440\u0434\u0435 \u043a\u04e9\u0440\u0441\u0435\u0442\u0443 \u2014 \u043e\u049b\u0443\u0448\u044b\u043d\u044b\u04a3 \u0435\u0441\u0442\u0435 \u0441\u0430\u049b\u0442\u0430\u0443\u044b\u043d \u0436\u0430\u049b\u0441\u0430\u0440\u0442\u0430\u0434\u044b. \u041c\u044b\u0441\u0430\u043b\u044b, \u043d\u04af\u043a\u0442\u0435\u043b\u0435\u0440\u0434\u0456 \u0436\u044b\u043b\u0436\u044b\u0442\u044b\u043f, \u0432\u0435\u043a\u0442\u043e\u0440\u0434\u044b\u04a3 \u04e9\u0437\u0433\u0435\u0440\u0456\u0441\u0456\u043d \u0431\u0456\u0440\u0434\u0435\u043d \u043a\u04e9\u0440\u0441\u0435\u0442\u0443.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u041c\u044b\u0441\u0430\u043b \u0435\u0441\u0435\u043f:<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u041c\u044b\u0441\u0430\u043b:<\/h4>\n\n\n\n<p>\u0411\u0435\u0440\u0456\u043b\u0433\u0435\u043d:<\/p>\n\n\n\n<p>A(1,2,3),B(4,6,7)<\/p>\n\n\n\n<p>\u0412\u0435\u043a\u0442\u043e\u0440 AB\u20d7=(?)\\vec{AB} = (?)<\/p>\n\n\n\n<p><strong>\u0428\u0435\u0448\u0443\u0456:<\/strong><\/p>\n\n\n\n<p>AB\u20d7=(4\u22121;\u2005\u200a6\u22122;\u2005\u200a7\u22123)=(3;\u2005\u200a4;\u2005\u200a4)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u049a\u0430\u0441\u0438\u0435\u0442\u0442\u0435\u0440:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0412\u0435\u043a\u0442\u043e\u0440 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043b\u0430\u0440\u044b \u2013 \u0431\u0430\u0493\u044b\u0442\u0442\u0430\u043b\u0493\u0430\u043d \u043a\u0435\u0441\u0456\u043d\u0434\u0456\u043d\u0456\u04a3 \u043f\u0440\u043e\u0435\u043a\u0446\u0438\u044f\u043b\u0430\u0440\u044b.<\/li>\n\n\n\n<li>\u0412\u0435\u043a\u0442\u043e\u0440 \u043c\u043e\u0434\u0443\u043b\u0456:<\/li>\n<\/ul>\n\n\n\n<p>\u2223a\u20d7\u2223=ax2+ay2+az2|<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"> <strong>\u0412\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0438\u0434\u0435\u044f\u0441\u044b:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u041d\u04af\u043a\u0442\u0435\u043b\u0435\u0440\u0434\u0456 3D \u043a\u0435\u04a3\u0456\u0441\u0442\u0456\u043a\u0442\u0435 \u043a\u04e9\u0440\u0441\u0435\u0442\u0456\u043f, \u0430\u0440\u0430\u043b\u0430\u0440\u044b\u043d\u0434\u0430\u0493\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0434\u044b \u0441\u044b\u0437\u0443.<\/li>\n\n\n\n<li>\u041e\u049b\u0443\u0448\u044b \u04e9\u0437\u0456 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0435\u043d\u0433\u0456\u0437\u0456\u043f, \u0432\u0435\u043a\u0442\u043e\u0440 \u043c\u0435\u043d \u043e\u043d\u044b\u04a3 \u04b1\u0437\u044b\u043d\u0434\u044b\u0493\u044b\u043d \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0442\u044b \u0442\u04af\u0440\u0434\u0435 \u043a\u04e9\u0440\u0435\u0434\u0456.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"974\" height=\"974\" src=\"https:\/\/makpal.studyedu.kz\/wp-content\/uploads\/2025\/04\/WhatsApp-Image-2025-04-07-at-18.08.06.jpeg\" alt=\"\" class=\"wp-image-62\" srcset=\"https:\/\/makpal.studyedu.kz\/wp-content\/uploads\/2025\/04\/WhatsApp-Image-2025-04-07-at-18.08.06.jpeg 974w, https:\/\/makpal.studyedu.kz\/wp-content\/uploads\/2025\/04\/WhatsApp-Image-2025-04-07-at-18.08.06-300x300.jpeg 300w, https:\/\/makpal.studyedu.kz\/wp-content\/uploads\/2025\/04\/WhatsApp-Image-2025-04-07-at-18.08.06-150x150.jpeg 150w, https:\/\/makpal.studyedu.kz\/wp-content\/uploads\/2025\/04\/WhatsApp-Image-2025-04-07-at-18.08.06-768x768.jpeg 768w\" sizes=\"(max-width: 974px) 100vw, 974px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u041c\u0430\u049b\u0441\u0430\u0442\u044b: \u041e\u049b\u0443\u0448\u044b\u043d\u044b \u043a\u0435\u04a3\u0456\u0441\u0442\u0456\u043a\u0442\u0435\u0433\u0456 \u0435\u043a\u0456 \u043d\u04af\u043a\u0442\u0435 \u0430\u0440\u049b\u044b\u043b\u044b \u0432\u0435\u043a\u0442\u043e\u0440 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043b\u0430\u0440\u044b\u043d \u0442\u0430\u0431\u0443\u0493\u0430 \u04af\u0439\u0440\u0435\u0442\u0443. \u0422\u0435\u043e\u0440\u0438\u044f\u043d\u044b \u0442\u0456\u0440\u0435\u043a \u0441\u044b\u0437\u0431\u0430 \u0436\u04d9\u043d\u0435 \u043c\u044b\u0441\u0430\u043b\u0434\u0430\u0440 \u0430\u0440\u049b\u044b\u043b\u044b \u0431\u0435\u043a\u0456\u0442\u0443. \u049a\u044b\u0441\u049b\u0430\u0448\u0430 \u0442\u0435\u043e\u0440\u0438\u044f: \u0412\u0435\u043a\u0442\u043e\u0440 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043b\u0430\u0440\u044b \u0434\u0435\u0433\u0435\u043d \u043d\u0435? \u041a\u0435\u04a3\u0456\u0441\u0442\u0456\u043a\u0442\u0435\u0433\u0456 \u0435\u043a\u0456 \u043d\u04af\u043a\u0442\u0435 A(x1,y1,z1)\u0436\u04d9\u043d\u0435 B(x2,y2,z2) \u0431\u0435\u0440\u0456\u043b\u0441\u0435,\u0432\u0435\u043a\u0442\u043e\u0440 AB\u20d7\\vec{AB} \u043a\u0435\u043b\u0435\u0441\u0456\u0434\u0435\u0439 \u0442\u0430\u0431\u044b\u043b\u0430\u0434\u044b: AB\u20d7=(x2\u2212x1;\u2005\u200ay2\u2212y1;\u2005\u200az2\u2212z1) \u0412\u0435\u043a\u0442\u043e\u0440 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u0441\u044b\u043d\u044b\u04a3 \u0436\u0430\u043b\u043f\u044b \u0431\u0435\u043b\u0433\u0456\u043b\u0435\u043d\u0443\u0456: \u0412\u0435\u043a\u0442\u043e\u0440 a\u20d7=(ax,ay,az) \u0422\u0456\u0440\u0435\u043a \u0441\u044b\u0437\u0431\u0430 (\u0431\u043b\u043e\u043a-\u0441\u0445\u0435\u043c\u0430): \u0411\u04b1\u043b \u0442\u0456\u0440\u0435\u043a \u0441\u044b\u0437\u0431\u0430\u043d\u044b \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u0442\u0456 \u0442\u04af\u0440\u0434\u0435 \u043a\u04e9\u0440\u0441\u0435\u0442\u0443 \u2014 \u043e\u049b\u0443\u0448\u044b\u043d\u044b\u04a3 \u0435\u0441\u0442\u0435 \u0441\u0430\u049b\u0442\u0430\u0443\u044b\u043d \u0436\u0430\u049b\u0441\u0430\u0440\u0442\u0430\u0434\u044b. \u041c\u044b\u0441\u0430\u043b\u044b, \u043d\u04af\u043a\u0442\u0435\u043b\u0435\u0440\u0434\u0456 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-34","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/pages\/34","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=34"}],"version-history":[{"count":4,"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/pages\/34\/revisions"}],"predecessor-version":[{"id":101,"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/pages\/34\/revisions\/101"}],"wp:attachment":[{"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}