{"id":28,"date":"2025-04-07T10:37:38","date_gmt":"2025-04-07T10:37:38","guid":{"rendered":"https:\/\/makpal.studyedu.kz\/?page_id=28"},"modified":"2025-05-13T05:39:49","modified_gmt":"2025-05-13T05:39:49","slug":"%d0%bc%d0%b0%d2%9b%d1%81%d0%b0%d1%82%d1%8b","status":"publish","type":"page","link":"https:\/\/makpal.studyedu.kz\/?page_id=28","title":{"rendered":"\u0412\u0435\u043a\u0442\u043e\u0440\u043b\u0430\u0440\u0434\u044b\u04a3 \u0430\u0440\u0430\u0441\u044b\u043d\u0434\u0430\u0493\u044b \u0431\u04b1\u0440\u044b\u0448\u0442\u044b \u0430\u043d\u044b\u049b\u0442\u0430\u0443"},"content":{"rendered":"\n<p>\u0412\u0435\u043a\u0442\u043e\u0440\u043b\u0430\u0440\u0434\u044b\u04a3 \u0430\u0440\u0430\u0441\u044b\u043d\u0434\u0430\u0493\u044b \u0431\u04b1\u0440\u044b\u0448\u0442\u044b \u0430\u043d\u044b\u049b\u0442\u0430\u0443 \u0436\u043e\u043b\u044b\u043d \u0436\u04d9\u043d\u0435 \u0441\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0441\u044b\u043d \u043c\u0435\u04a3\u0433\u0435\u0440\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<h4 class=\"wp-block-heading\"> \u0421\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456 \u0434\u0435\u0433\u0435\u043d\u0456\u043c\u0456\u0437 \u043d\u0435?<\/h4>\n\n\n\n<p>\u0415\u043a\u0456 \u0432\u0435\u043a\u0442\u043e\u0440\u0434\u044b\u04a3 \u0441\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456\u0441\u0456 \u2013 \u0441\u043e\u043b \u0432\u0435\u043a\u0442\u043e\u0440\u043b\u0430\u0440\u0434\u044b\u04a3 \u043c\u043e\u0434\u0443\u043b\u044c\u0434\u0435\u0440\u0456\u043d\u0456\u04a3 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456\u0441\u0456\u043d\u0435, \u0436\u04d9\u043d\u0435 \u043e\u043b\u0430\u0440\u0434\u044b\u04a3 \u0430\u0440\u0430\u0441\u044b\u043d\u0434\u0430\u0493\u044b \u0431\u04b1\u0440\u044b\u0448\u0442\u044b\u04a3 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u044b\u043d\u0430 \u0442\u0435\u04a3 \u0448\u0430\u043c\u0430.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u0424\u043e\u0440\u043c\u0443\u043b\u0430:<\/h4>\n\n\n\n<p>\u0415\u043a\u0456 \u0432\u0435\u043a\u0442\u043e\u0440:<\/p>\n\n\n\n<p>a\u20d7=(ax,ay,az),b\u20d7=(bx,by,bz)<\/p>\n\n\n\n<p>\u0421\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456:<\/p>\n\n\n\n<p>a\u20d7\u22c5b\u20d7=axbx+ayby+azbz<\/p>\n\n\n\n<p>\u0411\u04b1\u0440\u044b\u0448 \u0442\u0430\u0431\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0441\u044b:<\/p>\n\n\n\n<p>cos\u2061(\u03b8)=a\u20d7\u22c5b\u20d7\u2223a\u20d7\u2223\u22c5\u2223b\u20d7\u2223<\/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<h3 class=\"wp-block-heading\"><\/h3>\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\u20d7=(2,3,\u22121),b\u20d7=(1,\u22122,4)<\/p>\n\n\n\n<p><strong>\u0430) \u0421\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456\u0441\u0456\u043d \u0442\u0430\u0431\u044b\u04a3\u0434\u0430\u0440<\/strong><\/p>\n\n\n\n<p>a\u20d7\u22c5b\u20d7=2\u22c51+3\u22c5(\u22122)+(\u22121)\u22c54=2\u22126\u22124=\u22128<\/p>\n\n\n\n<p><strong>\u0431) \u0411\u04b1\u0440\u044b\u0448\u044b\u043d \u0442\u0430\u0431\u044b\u04a3\u0434\u0430\u0440:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u0412\u0435\u043a\u0442\u043e\u0440 \u043c\u043e\u0434\u0443\u043b\u044c\u0434\u0435\u0440\u0456:<\/li>\n<\/ol>\n\n\n\n<p>\u2223a\u20d7\u2223=22+32+(\u22121)2=4+9+1=14<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0411\u04b1\u0440\u044b\u0448:<\/li>\n<\/ul>\n\n\n\n<p>cos\u2061(\u03b8)=\u2212814\u22c521\u2248\u22120.467<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u03b8\u2248cos\u2061\u22121(\u22120.467)\u2248117.9<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"> <strong>\u0422\u04af\u0441\u0456\u043d\u0434\u0456\u0440\u0443 \u04af\u0448\u0456\u043d \u0432\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>\u0412\u0435\u043a\u0442\u043e\u0440\u043b\u0430\u0440 \u0430\u0440\u0430\u0441\u044b\u043d\u0434\u0430\u0493\u044b \u0431\u04b1\u0440\u044b\u0448\u0442\u044b \u0438\u043d\u0442\u0435\u0440\u0430\u043a\u0442\u0438\u0432\u0442\u0456 3D-\u0433\u0440\u0430\u0444\u0438\u043a\u0430\u043c\u0435\u043d \u043a\u04e9\u0440\u0441\u0435\u0442\u0443.<\/li>\n\n\n\n<li>\u041a\u04e9\u043b\u0431\u0435\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043b\u0430\u0440\u0434\u044b \u0431\u04b1\u0440\u0443 \u0430\u0440\u049b\u044b\u043b\u044b \u0431\u04b1\u0440\u044b\u0448\u0442\u044b \u04e9\u0437\u0433\u0435\u0440\u0442\u0443 \u2014 \u043e\u049b\u0443\u0448\u044b \u0442\u04d9\u0436\u0456\u0440\u0438\u0431\u0435 \u0436\u0430\u0441\u0430\u0439 \u0430\u043b\u0430\u0434\u044b.<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412\u0435\u043a\u0442\u043e\u0440\u043b\u0430\u0440\u0434\u044b\u04a3 \u0430\u0440\u0430\u0441\u044b\u043d\u0434\u0430\u0493\u044b \u0431\u04b1\u0440\u044b\u0448\u0442\u044b \u0430\u043d\u044b\u049b\u0442\u0430\u0443 \u0436\u043e\u043b\u044b\u043d \u0436\u04d9\u043d\u0435 \u0441\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0441\u044b\u043d \u043c\u0435\u04a3\u0433\u0435\u0440\u0442\u0443 \u049a\u044b\u0441\u049b\u0430\u0448\u0430 \u0442\u0435\u043e\u0440\u0438\u044f: \u0421\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456 \u0434\u0435\u0433\u0435\u043d\u0456\u043c\u0456\u0437 \u043d\u0435? \u0415\u043a\u0456 \u0432\u0435\u043a\u0442\u043e\u0440\u0434\u044b\u04a3 \u0441\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456\u0441\u0456 \u2013 \u0441\u043e\u043b \u0432\u0435\u043a\u0442\u043e\u0440\u043b\u0430\u0440\u0434\u044b\u04a3 \u043c\u043e\u0434\u0443\u043b\u044c\u0434\u0435\u0440\u0456\u043d\u0456\u04a3 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456\u0441\u0456\u043d\u0435, \u0436\u04d9\u043d\u0435 \u043e\u043b\u0430\u0440\u0434\u044b\u04a3 \u0430\u0440\u0430\u0441\u044b\u043d\u0434\u0430\u0493\u044b \u0431\u04b1\u0440\u044b\u0448\u0442\u044b\u04a3 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u044b\u043d\u0430 \u0442\u0435\u04a3 \u0448\u0430\u043c\u0430. \u0424\u043e\u0440\u043c\u0443\u043b\u0430: \u0415\u043a\u0456 \u0432\u0435\u043a\u0442\u043e\u0440: a\u20d7=(ax,ay,az),b\u20d7=(bx,by,bz) \u0421\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456: a\u20d7\u22c5b\u20d7=axbx+ayby+azbz \u0411\u04b1\u0440\u044b\u0448 \u0442\u0430\u0431\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0441\u044b: cos\u2061(\u03b8)=a\u20d7\u22c5b\u20d7\u2223a\u20d7\u2223\u22c5\u2223b\u20d7\u2223 \u0422\u0456\u0440\u0435\u043a \u0441\u044b\u0437\u0431\u0430 (\u0431\u043b\u043e\u043a-\u0441\u0445\u0435\u043c\u0430): \u041c\u044b\u0441\u0430\u043b \u0435\u0441\u0435\u043f: \u041c\u044b\u0441\u0430\u043b: \u0411\u0435\u0440\u0456\u043b\u0433\u0435\u043d: a\u20d7=(2,3,\u22121),b\u20d7=(1,\u22122,4) \u0430) \u0421\u043a\u0430\u043b\u044f\u0440 \u043a\u04e9\u0431\u0435\u0439\u0442\u0456\u043d\u0434\u0456\u0441\u0456\u043d \u0442\u0430\u0431\u044b\u04a3\u0434\u0430\u0440 [&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-28","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/pages\/28","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=28"}],"version-history":[{"count":5,"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/pages\/28\/revisions"}],"predecessor-version":[{"id":103,"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=\/wp\/v2\/pages\/28\/revisions\/103"}],"wp:attachment":[{"href":"https:\/\/makpal.studyedu.kz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}