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{"save":1,"level":1,"time":"90","total":34,"point":5,"segment":[{"id":"3816","test_id":"480","question":"<p>Trong không gian Oxyz, ph\u01b0\u01a1ng trình m\u1eb7t ph\u1eb3ng \u0111i qua \u0111i\u1ec3m M(1; –2; 3) và có vect\u01a1 pháp tuy\u1ebfn <span class=\"math-tex\">$\\overrightarrow{n}=(2;0;1)$<\/span> là<\/p>","options":["A. 2y + z + 1 = 0","B. 2x + z – 5 = 0","C. 2x + y = 0","D. x – 2y + 3z – 5 = 0"],"correct":"2","answer":"<p>\u0110áp án \u0111úng là: <strong><span style=\"color:#16a085;\">B. 2x + z – 5 = 0.<\/span><\/strong><span style=\"color:#16a085;\"><\/span><\/p><p>Ph\u01b0\u01a1ng trình m\u1eb7t ph\u1eb3ng \u0111i qua \u0111i\u1ec3m M(1; –2; 3) và có vect\u01a1 pháp tuy\u1ebfn <span class=\"math-tex\">$\\overrightarrow{n}=(2;0;1)$<\/span> là<\/p><p><span class=\"math-tex\">$2(x-1)+0(y+2)+1(z-3)=0$<\/span> ⇔ <span class=\"math-tex\">$2x+z-5=0$<\/span>.<\/p>","type":"choose","user_id":"126","test":"2","date":"2025-05-13 15:19:33"},{"id":"3818","test_id":"480","question":"<p>Cho hình chóp S.ABC có \u0111áy ABC là tam giác vuông cân t\u1ea1i A. G\u1ecdi các \u0111i\u1ec3m M, N l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a SB và SC. Khi \u0111ó góc gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng MN và AB.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$90^\\circ$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$60^\\circ$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$45^\\circ$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$30^\\circ$<\/span>"],"correct":"3","answer":"<p>\u0110áp án \u0111úng là: <span style=\"color:#16a085;\"><strong>C. <span class=\"math-tex\">$45^\\circ$<\/span>.<\/strong><\/span><\/p><p><span class=\"svgedit\"><svg height=\"210\" width=\"240\"> <g>\\n<title><\/title>\\n<rect fill=\"#fff\" height=\"212\" id=\"canvas_background\" width=\"242\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_3\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g>\\n<title><\/title>\\n<g id=\"svg_27\"> <g id=\"svg_8\"> <path d=\"m70.59499,181.35986l143.99999,-60l-193.99999,-1l50,61z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#ffffff\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"2\" x1=\"35\" x2=\"193.99999\" y1=\"120.65\" y2=\"121.65\"><\/line> <line fill=\"none\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"92.99999\" x2=\"21\" y1=\"21.65\" y2=\"119.65\"><\/line> <line fill=\"none\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"214.99999\" x2=\"93\" y1=\"120.65\" y2=\"20.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"93.99999\" x2=\"71\" y1=\"20.65\" y2=\"181.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"55\" x2=\"157.99999\" y1=\"74\" y2=\"73.65\"><\/line> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"66\" x2=\"74\" y1=\"46.65\" y2=\"55.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"37\" x2=\"45\" y1=\"86.65\" y2=\"95.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_11\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"121\" x2=\"131\" y1=\"53.65\" y2=\"42.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"125\" x2=\"135\" y1=\"56.65\" y2=\"45.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"169\" x2=\"179\" y1=\"92.65\" y2=\"81.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_14\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"173\" x2=\"183\" y1=\"94.65\" y2=\"83.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_15\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"39\" x2=\"57\" y1=\"156.65\" y2=\"152.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_16\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"48\" x2=\"49\" y1=\"143.65\" y2=\"163.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_17\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"132\" x2=\"148\" y1=\"145.65\" y2=\"157.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_18\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"137\" x2=\"142\" y1=\"158.65\" y2=\"144.65\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_19\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"73\" xml:space=\"preserve\" y=\"22.65\">S<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_20\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"1\" xml:space=\"preserve\" y=\"125.65\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_21\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"62\" xml:space=\"preserve\" y=\"202.64999\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_22\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"215.99999\" xml:space=\"preserve\" y=\"129.65\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_23\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"32\" xml:space=\"preserve\" y=\"74.65\">M<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_24\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"160\" xml:space=\"preserve\" y=\"73.65\">N<\/text> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_25\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"64\" x2=\"78\" y1=\"172.65\" y2=\"166.65\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_26\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"78\" x2=\"84\" y1=\"165.65\" y2=\"174.65\"><\/line> <\/g> <\/g> <\/svg><\/span><\/p><p>Xét tam giác SBC có M là trung \u0111i\u1ec3m SB, N là trung \u0111i\u1ec3m SC nên MN là \u0111\u01b0\u1eddng trung bình c\u1ee7a tam giác SBC \u1ee9ng v\u1edbi c\u1ea1nh BC.<\/p><p>Suy ra MN \/\/ BC.<\/p><p>Do \u0111ó (MN, AB) = (BC, AB) = <span class=\"math-tex\">$\\widehat{ABC}$<\/span> = 45° (vì tam giác ABC vuông cân t\u1ea1i A).<\/p>","type":"choose","user_id":"126","test":"2","date":"2025-05-13 15:22:16"}]}