{"common":{"save":0,"post_id":"8735","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6293","post_id":"8735","mon_id":"1159285","chapter_id":"1159382","question":"<p>Cho ba \u0111i\u1ec3m A(3;0;0), B(0;–6;0), C(0;2;–3). Tính kho\u1ea3ng cách d t\u1eeb tr\u1ecdng tâm G c\u1ee7a tam giác ABC \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (Oxy).<\/p>","options":["<strong>A.<\/strong> d = 2","<strong>B.<\/strong> d = 3","<strong>C.<\/strong> d = 1","<strong>D.<\/strong> d = 4"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> d = 1.<\/span><\/p><p>M\u1eb7t ph\u1eb3ng (Oxy): z = 0.<\/p><p>Vì G là tr\u1ecdng tâm tam giác ABC nên <span class=\"math-tex\">$G\\bigg(1;-\\dfrac{4}{3};-1\\bigg)$<\/span>.<\/p><p>V\u1eady kho\u1ea3ng cách t\u1eeb G \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (Oxy) là d = |–1| =1.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-04-03 08:39:42","option_type":"txt","len":0},{"id":"6294","post_id":"8735","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz, cho m\u1eb7t c\u1ea7u <span class=\"math-tex\">$(S):(x-1)^2+(y+2)^2+(z-3)^2=25$<\/span>. T\u1ecda \u0111\u1ed9 tâm I và bán kính R c\u1ee7a m\u1eb7t c\u1ea7u (S) là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$I(1;-2;3),\\;R=5$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$I(-1;2;-3),\\;R=5$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$I(1;-2;3),\\;R=25$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$I(-1;2;-3),\\;R=25$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$I(1;-2;3),\\;R=5$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$(S):(x-1)^2+(y+2)^2+(z-3)^2=25$<\/span> có tâm <span class=\"math-tex\">$I(1;-2;3)$<\/span> và bán kính R = 5.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-04-03 08:43:30","option_type":"math","len":0},{"id":"6297","post_id":"8735","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz, cho hai \u0111i\u1ec3m A(1;0;–2) và B(5;4;4). Ph\u01b0\u01a1ng trình m\u1eb7t c\u1ea7u \u0111\u01b0\u1eddng kính AB là<\/p>","options":["<strong>A.<\/strong> (x + 3)² + (y + 2)² + (z + 1)² = 17","<strong>B.<\/strong> (x – 3)² + (y – 2)² + (z – 1)² = 17","<strong>C.<\/strong> (x + 3)² + (y + 2)² + (z + 1)² = 34","<strong>D.<\/strong> (x – 3)² + (y – 2)² + (z – 1)² = 34"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> (x – 3)² + (y – 2)² + (z – 1)² = 17.<\/span><\/p><p>G\u1ecdi I là trung \u0111i\u1ec3m c\u1ee7a AB. Khi \u0111ó I(3 ; 2 ; 1) là tâm c\u1ee7a m\u1eb7t c\u1ea7u \u0111\u01b0\u1eddng kinh AB.<\/p><p>Bán kính m\u1eb7t c\u1ea7u R = AB : 2 = <span class=\"math-tex\">$\\sqrt{(5-1)^2+(4-0)^2+(4+2)^2}:2$<\/span> = <span class=\"math-tex\">$\\sqrt{17}$<\/span>.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình m\u1eb7t c\u1ea7u \u0111\u01b0\u1eddng kính AB là (x – 3)² + (y – 2)² + (z – 1)² = 17.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-04-03 08:50:09","option_type":"txt","len":3}]}