Trong không gian với hệ tọa độ Oxyz, cho ba đường thẳng . Viết phương trình mặt phẳng đi qua điểm  và cắt ba đường thẳng  lần lượt tại A , B , C sao cho H là trực tâm tam giác ABC .         

Trong không gian , mặt phẳng đi qua điểm  và vuông góc với đường thẳng  có phương trình là

Tìm một vectơ pháp tuyến của mặt phẳng có phương trình    

Trong không gian  cho các điểm   và  Mặt phẳng  đi qua các điểm  sao cho khoảng cách từ điểm  đến  gấp sáu lần khoảng cách từ điểm  đến  Có bao nhiêu mặt phẳng  thỏa mãn đề bài? 

Trong không gian cho 3 điểm và mặt cầu Viết phương trình mặt phẳng đi qua qua  song song với và tiếp xúc với mặt cầu có tâm và có bán kính  

Trong không gian với hệ tọa độ , cho điểm  và mặt phẳng . Phương trình nào dưới đây là phương trình mặt phẳng đi qua  và song song với ?         

Trong không gian với hệ tọa độ Oxyz, tìm một véctơ pháp tuyến của mặt phẳng

Phương trình mặt phẳng quavà vuông góc với mặt phẳng .  

Cho mặt phẳng . Khi đó, một véc – tơ pháp tuyến của mặt phẳng  là

Trong không gian , cho ba điểm , , . Mặt phẳng  có phương trình là

Trong không gian với hệ tọa độ , cho mặt phẳng . Mặt phẳng vuông góc với và cách điểm một khoảng bằng có dạng với . Ta có kết luận gì về ?

Cho mặt phẳng  đi qua các điểm , , . Mặt phẳng vuông góc với mặt phẳng nào trong các mặt phẳng sau?  

Trong không gian tọa độ Oxyz, cho đường thẳng và điểm . Viết phương trình mặt phẳng chứa d và đi qua A

Trong không gian với hệ trục tọa độ Oxyz cho hai điểm và mặt phẳng (P) có phương trình: . Phương trình mặt phẳng đi qua hai điểm và tạo với mặt phẳng một góc nhỏ nhất có phương trình là

(Mã đề 104 BGD&ĐT NĂM 2018) Trong không gian Oxyz, cho mặt cầu $\left(S\right):{\left(x-2\right)}^2+{\left(y-3\right)}^2+{\left(z+1\right)}^2=16$ và điểm $A\left(-1;-1;-1\right).$ Xét các điểm M thuộc $\left(S\right)$ sao cho đường thẳng AM tiếp xúc với $\left(S\right).$ M luôn thuộc một mặt phẳng cố định có phương trình là

Trong không gian với hệ trục tọa độ Oxyz, cho đường thẳng d đi qua hai điểm và có vectơ chỉ phương ; điểm . Phương trình mặt phẳng (P) chứa đường thẳng d có vectơ pháp tuyến là ?           

Mặt phẳng (P) chứa Oz và tạo với mặt phẳng một góc có phương trình là :  

Trong không gian với hệ trục tọa độ Oxyz cho hai điểm và mặt phẳng (P) có phương trình: . Phương trình mặt phẳng đi qua hai điểm và tạo với mặt phẳng một góc nhỏ nhất có phương trình là

Viết phương trình mặt phẳng qua , vuông góc với hai mặt phẳng   .  

Trong không gian với hệ tọa độ Oxyz , cho mặt phẳng . Vecto pháp tuyến  của mặt phẳng (P) là:  

Trong không gian với hệ tọa độ cho điểm Viết phương trình mặt phẳng đi qua các hình chiếu của trên các trục tọa độ.  

Trong không gian , cho , , , . Gọi  là mặt phẳng song song với ,  cách đều  và mặt phẳng . Phương trình của  là

Trong không gian Oxyz cho cho hai mặt phẳng (P): và (Q): . Tìm khẳng định đúng.  

Trong không gian Oxyz cho 5 điểm ; ; ; ; . Hỏi từ 5 điểm này tạo thành bao nhiêu mặt phẳng:

Trong không gian với hệ trục tọa độ Oxyz, viết phương trình mặt phẳng song song và cách đều hai đường thẳng .

Trong không gian với hệ tọa độ cho mặt cầu có phương trình . Phương trình mặt phẳng chứa trục hoành và tiếp xúc với mặt cầu là:

Trong không gian với hệ tọa độ Oxyz cho hai điểm  và mặt phẳng . Mặt phẳng (Q) chứa A, B và vuông góc với mặt phẳng (P) có phương trình là:            

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 24 to 28:

Few people now realize the reality of global warming and its effects on the world’s climate. Many scientists (24) _______ the blame for recent natural disasters on the increase in the world’s temperatures and are convinced that, more than ever before, the Earth is at (25) _______ from the forces of the wind, rain and sun. According to them, global warming is making extreme weather events, such as hurricanes and droughts, even more severe and causing sea levels all around the world to rise. Environmental groups are putting pressure on governments to take action to reduce the amount of carbon dioxide which is given (26) _______ by factories and power plants, thus attacking the problem at its source. They are in (27) _______ of more money being spent on research into solar, wind, and wave energy devices, which could then replace existing power (28) _______. Some scientists, however, believe that even if we stopped releasing carbon dioxide and other gases into the atmosphere tomorrow, we would have to wait several hundred years to notice the results. Global warming, it seems, is to stay.

Question 26:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 24 to 28:

Few people now realize the reality of global warming and its effects on the world’s climate. Many scientists (24) _______ the blame for recent natural disasters on the increase in the world’s temperatures and are convinced that, more than ever before, the Earth is at (25) _______ from the forces of the wind, rain and sun. According to them, global warming is making extreme weather events, such as hurricanes and droughts, even more severe and causing sea levels all around the world to rise. Environmental groups are putting pressure on governments to take action to reduce the amount of carbon dioxide which is given (26) _______ by factories and power plants, thus attacking the problem at its source. They are in (27) _______ of more money being spent on research into solar, wind, and wave energy devices, which could then replace existing power (28) _______. Some scientists, however, believe that even if we stopped releasing carbon dioxide and other gases into the atmosphere tomorrow, we would have to wait several hundred years to notice the results. Global warming, it seems, is to stay.

Question 28:       

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 15 to 19:

Fashions have always changed with time. No (15) ________ Roman girls worried about having the latest hairstyle and boys in Ancient Egypt wanted to have sandals that were cool and not the sensible ones their mothers preferred. Look (16) ________over recent times, there seem to be two main differences in the way fashions have changed compared to earlier time. Firstly, (17) ________ more people have a choice of clothes available to them. There are few places in the world where the trainers, the caps or the T-shirts of teenagers do not change from one year to the next. Secondly, styles are (18) ________within a much shorter time than they used to be. For instance, in the 1960s, (19) ________ had the same low waists and narrow skirts as forty years before. In the early years of the 21st century, the shops are full of long skirts and colored scarves like the ones in fashion only thirty years before. Soon, we will find that the really fashionable people look no different from the rest of us, because it is only ten years since their clothes were in fashion before!  

Question 15:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 27 to 38:

On a winter afternoon, a dozen male Northern fur seals are on an island off south - western Alaska. To look at them, fighting for territory on the rocks, it’s hard to imagine that they are at the (27)____________of a baffling scientific mystery: why is this species beginning to disappear? These seals - which can weigh up to 270 kilograms - have an important and symbolic (28)_________in Alaska’s history. Their soft and luxurious fur, the coveted prize during the huge commercial sea harvests that were legal here in the Bering Sea through the early 20th century, was once so valuable it (29)_________Alaska’s economy. Starting in the 1950s, for reasons that are (30)_______because the harvests by then tended to be fairly small, the seal population began a slow decline. But lately it has been falling drastically, declining at an alarming (31)________of 6 per cent a year since 1998. From a (32)_________ of more than 2 million in Alaska in 1948, their numbers have fallen to about 1 million. So (33)________, no one has been able to establish a precise cause for this, although theories (34)___________. The seal's food supply may be (35)________, or another species may be (36)________on the seals - perhaps killer whales, which no longer have as many great whales to eat because of harvesting of those mammals. Some people have suggested that the decline can be (37)______to entanglement in fishing nets, but scientists say they doubt that this alone could (38)_________the recent population decline.

Question 37:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 27 to 38:

On a winter afternoon, a dozen male Northern fur seals are on an island off south - western Alaska. To look at them, fighting for territory on the rocks, it’s hard to imagine that they are at the (27)____________of a baffling scientific mystery: why is this species beginning to disappear? These seals - which can weigh up to 270 kilograms - have an important and symbolic (28)_________in Alaska’s history. Their soft and luxurious fur, the coveted prize during the huge commercial sea harvests that were legal here in the Bering Sea through the early 20th century, was once so valuable it (29)_________Alaska’s economy. Starting in the 1950s, for reasons that are (30)_______because the harvests by then tended to be fairly small, the seal population began a slow decline. But lately it has been falling drastically, declining at an alarming (31)________of 6 per cent a year since 1998. From a (32)_________ of more than 2 million in Alaska in 1948, their numbers have fallen to about 1 million. So (33)________, no one has been able to establish a precise cause for this, although theories (34)___________. The seal's food supply may be (35)________, or another species may be (36)________on the seals - perhaps killer whales, which no longer have as many great whales to eat because of harvesting of those mammals. Some people have suggested that the decline can be (37)______to entanglement in fishing nets, but scientists say they doubt that this alone could (38)_________the recent population decline.

Question 36:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 27 to 38:

On a winter afternoon, a dozen male Northern fur seals are on an island off south - western Alaska. To look at them, fighting for territory on the rocks, it’s hard to imagine that they are at the (27)____________of a baffling scientific mystery: why is this species beginning to disappear? These seals - which can weigh up to 270 kilograms - have an important and symbolic (28)_________in Alaska’s history. Their soft and luxurious fur, the coveted prize during the huge commercial sea harvests that were legal here in the Bering Sea through the early 20th century, was once so valuable it (29)_________Alaska’s economy. Starting in the 1950s, for reasons that are (30)_______because the harvests by then tended to be fairly small, the seal population began a slow decline. But lately it has been falling drastically, declining at an alarming (31)________of 6 per cent a year since 1998. From a (32)_________ of more than 2 million in Alaska in 1948, their numbers have fallen to about 1 million. So (33)________, no one has been able to establish a precise cause for this, although theories (34)___________. The seal's food supply may be (35)________, or another species may be (36)________on the seals - perhaps killer whales, which no longer have as many great whales to eat because of harvesting of those mammals. Some people have suggested that the decline can be (37)______to entanglement in fishing nets, but scientists say they doubt that this alone could (38)_________the recent population decline.

Question 38:

Read the following passage and mark the letter A,B,C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks.

A trend that has emerged recently is the sharing of childcare (1) __________ between husband and wife. Young couples will try to arrange their work schedules so that they work opposite hours or shifts in order that one parent is always home with the children. Since childcare is expensive, this saves money for the young couple trying to establish themselves and provide a secure environment for the family. Husband and wife may also share household chores. Some fathers are just as capable as mothers at cooking dinner, changing and bathing the baby, and doing the laundry. In some cases, the woman’s salary is for family (2) __________ and the father becomes the “househusband." These cases are still fairly rare. One positive trend, however, is that fathers seem to be spending more time with their children. In a recent survey, 41% of the children sampled said they spend equal time with their mothers and fathers. “This is one of our most significant cultural changes,” says Dr. Leon Hoffman, who co-directs the Parent Child Center at the New York Psychoanalytic Society. In practice, for over 30 years, Hoffman has found "a very dramatic difference in the involvement of the father in everything from care-taking to general decision (3) __________ around kids' lives.” Another factor has recently been added to the childcare formula. The number of people who work from home nearly full-time rose 23% from the last decade. The (4) _________ of technology - computers, faxes, teleconferencing - has made it easier for at-home workers to be constantly in touch. Will this new flexibility in the workforce bring a positive change for the (5) __________ of children? Only time will tell.  

Question 1:

Read the following passage and mark the letter A,B,C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks.

A trend that has emerged recently is the sharing of childcare (1) __________ between husband and wife. Young couples will try to arrange their work schedules so that they work opposite hours or shifts in order that one parent is always home with the children. Since childcare is expensive, this saves money for the young couple trying to establish themselves and provide a secure environment for the family. Husband and wife may also share household chores. Some fathers are just as capable as mothers at cooking dinner, changing and bathing the baby, and doing the laundry. In some cases, the woman’s salary is for family (2) __________ and the father becomes the “househusband." These cases are still fairly rare. One positive trend, however, is that fathers seem to be spending more time with their children. In a recent survey, 41% of the children sampled said they spend equal time with their mothers and fathers. “This is one of our most significant cultural changes,” says Dr. Leon Hoffman, who co-directs the Parent Child Center at the New York Psychoanalytic Society. In practice, for over 30 years, Hoffman has found "a very dramatic difference in the involvement of the father in everything from care-taking to general decision (3) __________ around kids' lives.” Another factor has recently been added to the childcare formula. The number of people who work from home nearly full-time rose 23% from the last decade. The (4) _________ of technology - computers, faxes, teleconferencing - has made it easier for at-home workers to be constantly in touch. Will this new flexibility in the workforce bring a positive change for the (5) __________ of children? Only time will tell.  

Question 2:

Read the following passage and mark the letter A,B,C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks.

A trend that has emerged recently is the sharing of childcare (1) __________ between husband and wife. Young couples will try to arrange their work schedules so that they work opposite hours or shifts in order that one parent is always home with the children. Since childcare is expensive, this saves money for the young couple trying to establish themselves and provide a secure environment for the family. Husband and wife may also share household chores. Some fathers are just as capable as mothers at cooking dinner, changing and bathing the baby, and doing the laundry. In some cases, the woman’s salary is for family (2) __________ and the father becomes the “househusband." These cases are still fairly rare. One positive trend, however, is that fathers seem to be spending more time with their children. In a recent survey, 41% of the children sampled said they spend equal time with their mothers and fathers. “This is one of our most significant cultural changes,” says Dr. Leon Hoffman, who co-directs the Parent Child Center at the New York Psychoanalytic Society. In practice, for over 30 years, Hoffman has found "a very dramatic difference in the involvement of the father in everything from care-taking to general decision (3) __________ around kids' lives.” Another factor has recently been added to the childcare formula. The number of people who work from home nearly full-time rose 23% from the last decade. The (4) _________ of technology - computers, faxes, teleconferencing - has made it easier for at-home workers to be constantly in touch. Will this new flexibility in the workforce bring a positive change for the (5) __________ of children? Only time will tell.

Question 3:  

Read the following passage and mark the letter A,B,C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks.

A trend that has emerged recently is the sharing of childcare (1) __________ between husband and wife. Young couples will try to arrange their work schedules so that they work opposite hours or shifts in order that one parent is always home with the children. Since childcare is expensive, this saves money for the young couple trying to establish themselves and provide a secure environment for the family. Husband and wife may also share household chores. Some fathers are just as capable as mothers at cooking dinner, changing and bathing the baby, and doing the laundry. In some cases, the woman’s salary is for family (2) __________ and the father becomes the “househusband." These cases are still fairly rare. One positive trend, however, is that fathers seem to be spending more time with their children. In a recent survey, 41% of the children sampled said they spend equal time with their mothers and fathers. “This is one of our most significant cultural changes,” says Dr. Leon Hoffman, who co-directs the Parent Child Center at the New York Psychoanalytic Society. In practice, for over 30 years, Hoffman has found "a very dramatic difference in the involvement of the father in everything from care-taking to general decision (3) __________ around kids' lives.” Another factor has recently been added to the childcare formula. The number of people who work from home nearly full-time rose 23% from the last decade. The (4) _________ of technology - computers, faxes, teleconferencing - has made it easier for at-home workers to be constantly in touch. Will this new flexibility in the workforce bring a positive change for the (5) __________ of children? Only time will tell.  

Question 4: