Đường thẳng vuông góc với mặt phẳng

Home Lớp 11 Toán lớp 11 - Sách kết nối tri thức Bài 23. Đường thẳng vuông góc với mặt phẳng.Bài tập nâng cao

{"common":{"save":0,"post_id":"7122","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5515","post_id":"7122","mon_id":"1158924","chapter_id":"1159174","question":"Cho l\u0103ng tr\u1ee5 \u0111\u1ec1u ABC.A'B'C' có c\u1ea1nh \u0111áy b\u1eb1ng a, c\u1ea1nh bên b\u1eb1ng 2a. G\u1ecdi M là trung \u0111i\u1ec3m c\u1ee7a AB. Di\u1ec7n tích thi\u1ebft di\u1ec7n c\u1eaft l\u0103ng tr\u1ee5 \u0111ã cho b\u1edfi m\u1eb7t ph\u1eb3ng (A'C'M) là<\/p>","options":["A. <\/strong>$\\dfrac{7\\sqrt{2}}{16}a^2$<\/span>","B. <\/strong>$\\dfrac{3\\sqrt{35}}{16}a^2$<\/span>","C. <\/strong>$\\dfrac{3\\sqrt{2}}{4}a^2$<\/span>","D. <\/strong>$\\dfrac{9}{8}a^2$<\/span>"],"correct":"2","level":"3","hint":"","answer":"Ch\u1ecdn B. <\/strong>$\\dfrac{3\\sqrt{35}}{16}a^2$<\/span><\/span><\/p>G\u1ecdi N là trung \u0111i\u1ec3m BC. K\u1ebb MN \/\/ AC suy ra MN \/\/ A'C'.<\/p>Mp (A'C'M) c\u1eaft l\u0103ng tr\u1ee5 l\u1ea7n l\u01b0\u1ee3t theo thi\u1ebft di\u1ec7n là hình thang A'C'NM.<\/p>G\u1ecdi E, E' l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AC và A'C'. G\u1ecdi H là giao \u0111i\u1ec3m c\u1ee7a MN và BE.<\/p>Ta d\u1ec5 dàng ch\u1ee9ng minh \u0111\u01b0\u1ee3c MN &perp; (E'HE).<\/p>Ta có (A'C'NM) ∩ (ABC) = MN, EH &perp; MN, E'H &perp; MN. Suy ra <\/p>$((A’C’NM),(ACNM))=(HE, HE’)=\\widehat{E’HE}=\\phi$<\/span><\/p>Ta có: $BE=\\dfrac{a\\sqrt{3}}{2}$<\/span> ⇒ $HE=\\dfrac{a\\sqrt{3}}{4}$<\/span>. L\u1ea1i có $E’H=\\sqrt{E’E^2+EH^2}=\\sqrt{2a^2+\\dfrac{3a^2}{16}}=\\dfrac{a\\sqrt{35}}{16}$<\/span><\/p>T\u1eeb \u0111ó $\\cos\\phi=\\dfrac{HE}{HE’}=\\dfrac{a\\sqrt{3}}{4}.\\dfrac{4}{a\\sqrt{35}}=\\dfrac{\\sqrt{3}}{\\sqrt{35}}$<\/span><\/p>$S_{ACNM}=\\dfrac{(MN+AC).HE}{2}=\\dfrac{3a^2\\sqrt{3}}{16}$<\/span><\/p>$S_{A’C’NM}=\\dfrac{S_{ACNM}}{\\cos\\phi}=\\dfrac{3a^2\\sqrt{3}}{16}.\\dfrac{\\sqrt{35}}{\\sqrt{3}}=\\dfrac{3a^2\\sqrt{35}}{16}$<\/span><\/p><svg height=\"300\" width=\"400\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"302\" id=\"canvas_background\" width=\"402\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_8\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_7\"> <path d=\"m101.44182,92.63886l192.69816,-70l-255.99998,1l63.30182,69z\" fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <path 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<\/svg><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-21 03:22:23","option_type":"math","len":0},{"id":"5558","post_id":"7122","mon_id":"1158924","chapter_id":"1159174","question":"Cho hình chóp S.ABC có \u0111áy ABC là tam giác vuông t\u1ea1i C, SA = SB = SC. G\u1ecdi H là hình chi\u1ebfu vuông góc c\u1ee7a S trên (ABC) . Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây \u0111úng<\/strong>?<\/p>","options":["A.<\/strong> H là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AB","B.<\/strong> H là tr\u1ecdng tâm c\u1ee7a ΔABC","C.<\/strong> H là tr\u1ef1c tâm c\u1ee7a ΔABC","D.<\/strong> H là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AC"],"correct":"1","level":"3","hint":"","answer":"Ch\u1ecdn A.<\/strong> H là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AB<\/span><\/p>Xét các tam giác vuông ΔSHA, ΔSHB, ΔSHC có: $SA^2=SH^2+HA^2; SB^2=SH^2+HB^2;SC^2=SH^2+HC^2$<\/span> Mà SA = SB = SC nên HA = HB = HC. Do \u0111ó H là tâm \u0111\u01b0\u1eddng tròn ngo\u1ea1i ti\u1ebfp tam giác ABC. Vì ABC là tam giác vuông t\u1ea1i C nên H là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AB.<\/p><svg height=\"254\" width=\"242\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"256\" id=\"canvas_background\" width=\"244\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <image height=\"254.00001\" id=\"svg_1\" stroke=\"null\" width=\"241.99999\" x=\"0.5\" 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\" y=\"0.5\"><\/image> <\/g> <\/svg><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-01 05:15:45","option_type":"txt","len":2},{"id":"5560","post_id":"7122","mon_id":"1158924","chapter_id":"1159174","question":"Cho hình chóp S.ABC có $\\widehat{BSC}=120^o,\\widehat{CSA}=60^o,\\widehat{ASB}=90^o$<\/span>, SA = SB = SC. G\u1ecdi I là hình chi\u1ebfu vuông góc c\u1ee7a S trên (ABC) . Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây \u0111úng<\/strong>?<\/p>","options":["A.<\/strong> I là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AB","B.<\/strong> I là tr\u1ecdng tâm c\u1ee7a ABC","C.<\/strong> I là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC","D.<\/strong> I là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AC"],"correct":"3","level":"3","hint":"","answer":"Ch\u1ecdn C.<\/strong> I là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC<\/span><\/p>\u0110\u1eb7t SA = SB = SC = a.<\/p>Xét tam giác SBC có $BC^2=SB^2+SC^2-2.SB.SC.\\cos120^o=3a^2$<\/span><\/p>Xét tam giác SAB vuông t\u1ea1i S có $AB^2=SB^2+SA^2-2.SB.SC.\\cos120^o=3a^2$<\/span><\/p>Xét tam giác ABC có $BC^2=AB^2+AC^2=3a^2$<\/span> ⇒ ΔABC vuông t\u1ea1i A.<\/p>Xét các tam giác vuông SIA, SIB, SIC có $SA^2=SI^2+IA^2;SB^2=SI^2+IB^2;SC^2=SI^2+IC^2;$<\/span><\/p>Mà SA = SB = SC nên IA = IB = IC, Do \u0111ó I là tâm \u0111\u01b0\u1eddng trong ngo\u1ea1i ti\u1ebfm tam giác ABC. Vì tam giác ABC vuông nên I là trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC.<\/p><svg height=\"211\" width=\"206\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"213\" id=\"canvas_background\" width=\"208\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <image height=\"211\" id=\"svg_1\" width=\"206\" x=\"0\" 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\" 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