Đường thẳng và mặt phẳng song song

Home Lớp 11 Toán lớp 11 - Sách kết nối tri thức Bài 12. Đường thẳng và mặt phẳng song song.Bài tập cơ bản

{"common":{"save":0,"post_id":"7072","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5092","post_id":"7072","mon_id":"1158924","chapter_id":"1159156","question":"Cho \u0111\u01b0\u1eddng th\u1eb3ng a và m\u1eb7t ph\u1eb3ng (P) trong không gian. Có bao nhiêu v\u1ecb trí t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a a và (P)?<\/p>","options":["2","3","1","4"],"correct":"2","level":"1","hint":"","answer":"Ch\u1ecdn ngôi sao ch\u1ee9a s\u1ed1 3<\/strong><\/span>.<\/p>Có 3 v\u1ecb trí t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a a và (P), \u0111ó là:<\/p>+ a n\u1eb1m trong (P)<\/p>+ a song song v\u1edbi (P)<\/p>+ a c\u1eaft (P)<\/p> <svg height=\"100\" width=\"210\"> <g><title><\/title><rect fill=\"#fff\" height=\"102\" id=\"canvas_background\" width=\"212\" 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><g id=\"svg_15\"> <g id=\"svg_4\"> <path d=\"m5.88005,90.70007l39.40001,-81l157.6,0l-39.40001,81l-157.6,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"14\" xml:space=\"preserve\" y=\"83.65\">(P)<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"35\" id=\"svg_3\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-33.30332565307617 35.77541732788089,68.75654602050781) matrix(0.7974381798364141,0,0,1.3579123132657145,14.549316086173622,-28.573968516521106) \" x=\"20.78611\" xml:space=\"preserve\" y=\"83.89015\">)<\/text> <\/g> <g id=\"svg_7\"> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"47\" x2=\"163\" y1=\"46.65\" y2=\"46.65\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"150\" xml:space=\"preserve\" y=\"61.65\">a<\/text> <\/g> <\/g> <\/g> <\/svg><\/span>     <svg height=\"150\" width=\"210\"> <g><title><\/title><rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"212\" 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_4\"> <path d=\"m6.88005,131.70007l39.40001,-81l157.6,0l-39.40001,81l-157.6,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"15\" xml:space=\"preserve\" y=\"124.65\">(P)<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"35\" id=\"svg_3\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-33.30332565307617 36.77542495727545,109.75655364990236) matrix(0.7974381798364141,0,0,1.3579123132657145,14.549316086173622,-28.573968516521106) \" x=\"22.04013\" xml:space=\"preserve\" y=\"114.08356\">)<\/text> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"28\" x2=\"200\" y1=\"16.65\" y2=\"16.65\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"186\" xml:space=\"preserve\" y=\"32.65\">a<\/text> <\/g> <\/svg><\/span>     <svg height=\"150\" width=\"210\"> <g><title><\/title><rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"212\" 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_11\"> <g id=\"svg_4\"> <path d=\"m7.88005,116.70007l39.40001,-81l157.6,0l-39.40001,81l-157.6,0z\" fill=\"#fff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_2\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"16\" xml:space=\"preserve\" y=\"109.65\">(P)<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"35\" id=\"svg_3\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-33.30332565307617 37.77542495727543,94.75654602050781) matrix(0.7974381798364141,0,0,1.3579123132657145,14.549316086173622,-28.573968516521106) \" x=\"23.29415\" xml:space=\"preserve\" y=\"103.03719\">)<\/text> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(60 132.08734130859375,106.63269805908203) \" x1=\"92.21383\" x2=\"171.96085\" y1=\"106.6327\" y2=\"106.6327\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"85\" xml:space=\"preserve\" y=\"18.65\">a<\/text> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(60 94.08734130859372,40.63269805908204) \" x1=\"54.21383\" x2=\"133.96085\" y1=\"40.6327\" y2=\"40.6327\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#ffffff\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"1.5\" transform=\"rotate(60 124.45817565917969,93.41859436035158) \" x1=\"99.843\" x2=\"149.07336\" y1=\"93.4186\" y2=\"93.4186\"><\/line> <\/g> <ellipse cx=\"110.99999\" cy=\"69.65\" fill=\"#000000\" id=\"svg_12\" rx=\"2\" ry=\"2\" stroke=\"#000000\" stroke-width=\"1.5\"><\/ellipse> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_13\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"92\" xml:space=\"preserve\" y=\"78.65\">A<\/text> <\/g> <\/svg><\/span><\/p>","type":"choose","extra_type":"star","user_id":"131","test":"0","date":"2024-02-16 02:36:58","option_type":"txt","len":0},{"id":"5094","post_id":"7072","mon_id":"1158924","chapter_id":"1159156","question":"Cho hai \u0111\u01b0\u1eddng th\u1eb3ng phân bi\u1ec7t a, b và m\u1eb7t ph\u1eb3ng (P). Gi\u1ea3 s\u1eed a \/\/ (P), b ⊂ (P). Khi \u0111ó:<\/p>","options":["A.<\/strong> a \/\/ b","B.<\/strong> a, b chéo nhau","C.<\/strong> a \/\/ b ho\u1eb7c a, b chéo nhau","D.<\/strong> a, b c\u1eaft nhau"],"correct":"3","level":"1","hint":"","answer":"Ch\u1ecdn C.<\/strong> a \/\/ b ho\u1eb7c a, b chéo nhau<\/span><\/p>Vì a \/\/ (P) nên t\u1ed3n t\u1ea1i \u0111\u01b0\u1eddng th\u1eb3ng c ⊂ (P) th\u1ecfa mãn a \/\/ c. Suy ra b, c \u0111\u1ed3ng ph\u1eb3ng. Do \u0111ó x\u1ea3y ra các tr\u01b0\u1eddng h\u1ee3p sau:<\/p>+ N\u1ebfu b song song ho\u1eb7c trùng v\u1edbi c thì a \/\/ b.<\/p>+ N\u1ebfu b c\u1eaft c thì b c\u1eaft m\u1eb7t ph\u1eb3ng (a, c) nên a, b không \u0111\u1ed3ng ph\u1eb3ng. Do \u0111ó, a và b chéo nhau.<\/p>     <svg height=\"160\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"232\" 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><g id=\"svg_10\"> <g id=\"svg_7\"> <g id=\"svg_4\"> <path d=\"m4.835,152.78008l42.20001,-103l168.8,0l-42.20001,103l-168.8,0z\" fill=\"#d4ffaa\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"15\" xml:space=\"preserve\" y=\"147.65\">P<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"35\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-33.727840423583984 34.3226127624512,128.00486755371094) matrix(0.8097054362297058,0,0,1.5649380683898926,9.895316590139146,-90.55097105667664) \" x=\"24.33913\" xml:space=\"preserve\" y=\"151.53656\">)<\/text> <\/g> <line fill=\"none\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"48\" x2=\"182.99999\" y1=\"105.65\" y2=\"106\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"166\" xml:space=\"preserve\" y=\"125.65\">b<\/text> <\/g> <line fill=\"none\" id=\"svg_8\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"11\" x2=\"200.99999\" y1=\"25\" y2=\"24.65\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"183.89999\" xml:space=\"preserve\" y=\"20.65\">a<\/text> <\/g> <\/g> <\/svg><\/span>     <svg height=\"160\" width=\"230\"> <g><title><\/title><rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"232\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_11\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_4\"> <path d=\"m4.835,152.78008l42.20001,-103l168.8,0l-42.20001,103l-168.8,0z\" fill=\"#d4ffaa\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"15\" xml:space=\"preserve\" y=\"147.65\">P<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"35\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-33.727840423583984 34.32262802124029,128.00488281250003) matrix(0.8097054362297058,0,0,1.5649380683898926,9.895316590139146,-90.55097105667664) \" x=\"24.33913\" xml:space=\"preserve\" y=\"151.53656\">)<\/text> <\/g> <line fill=\"none\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"48\" x2=\"182.99999\" y1=\"105.65\" y2=\"106\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"78\" xml:space=\"preserve\" y=\"146.65\">b<\/text> <g id=\"svg_12\"> <line fill=\"none\" id=\"svg_8\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"11\" x2=\"200.99999\" y1=\"25\" y2=\"24.65\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"183.89999\" xml:space=\"preserve\" y=\"20.65\">a<\/text> <\/g> <line fill=\"none\" id=\"svg_13\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"177.89999\" x2=\"65.89999\" y1=\"62.65\" y2=\"139.64999\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_14\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"168.89999\" xml:space=\"preserve\" y=\"119.64999\">c<\/text> <\/g> <\/svg><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-16 02:51:15","option_type":"txt","len":2},{"id":"5095","post_id":"7072","mon_id":"1158924","chapter_id":"1159156","question":"Cho hai \u0111\u01b0\u1eddng th\u1eb3ng a, b phân bi\u1ec7t và m\u1eb7t ph\u1eb3ng (P). Gi\u1ea3 s\u1eed a \/\/ b và b ⊂ (P). Khi \u0111ó:<\/p>","options":["A.<\/strong> a \/\/ (P)","B.<\/strong> a ⊂ (P)","C.<\/strong> a c\u1eaft (P)","D.<\/strong> a \/\/ (P) ho\u1eb7c a ⊂ (P)"],"correct":"4","level":"1","hint":"","answer":"Ch\u1ecdn D.<\/strong> a \/\/ (P) ho\u1eb7c a ⊂ (P)<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-02-16 02:55:47","option_type":"txt","len":2}]}