Trong không gian Oxyz, cho tam giác ABC có \(A(2;-2;1)\) có trọng tâm G và M là trung điểm của cạnh B. Biết điểm \(G\) thuộc đường thẳng \(d:\frac{x-2}{1}=\frac{y+2}{2}=\frac{z+1}{2}\) và điểm \(M\) thuộc mặt phẳng \((P):x+2y-3z-1=0\). Đường thẳng AM có một vectơ chỉ phương là:
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Do \(G\in d\Rightarrow G(t+2;2t-2;2t-1)\).
\(\Rightarrow \overrightarrow{AG}=(t;2t;2t-2)\).
Do \(G\) là trọng tâm \(\Delta ABC\) nên \(\overrightarrow{AM}=\frac{3}{2}\overrightarrow{AG}\Rightarrow \overrightarrow{AM}=\left( \frac{3}{2}t;3t;3t-3 \right)\).
Do đó: \(M\left( \frac{3}{2}t+2;3t-2;3t-2 \right)\).
Do \(M\in (P)\) nên \(\frac{3}{2}t+2+2(3t-2)-3(3t-2)-1=0\Leftrightarrow t=2\).
\(\Rightarrow \overrightarrow{AM}=(3;6;3)\).
Vậy một vectơ chỉ phương của AM là \(\vec{u}=(1;2;1)\).
Đề Thi Minh Họa Đánh Giá Năng Lực Năm 2025 – ĐHQG Hà Nội – Đề Số 1 là bài thi được thiết kế hiện đại, đánh giá toàn diện ba nhóm năng lực cốt lõi: Giải Quyết Vấn Đề Và Sáng Tạo, Giao Tiếp Và Hợp Tác, Tự Chủ Và Tự Học. Với cấu trúc ba phần rõ ràng, thí sinh sẽ trải qua Toán Học Và Xử Lí Số Liệu/Tư Duy Định Lượng, Văn Học - Ngôn Ngữ/Tư Duy Định Tính và Khoa Học/Tiếng Anh. Từng câu hỏi trong đề thi không chỉ đánh giá kiến thức mà còn đo lường khả năng lập luận, tư duy logic, ngôn ngữ, tính toán, và cả kỹ năng tiếng Anh. Đây là cơ hội để học sinh thể hiện toàn diện năng lực học tập và khả năng phân tích, giải quyết vấn đề một cách khoa học và sáng tạo.
Câu hỏi liên quan
Read the following passage about the Reimagining International Cooperation and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Global environmental governance is changing how countries work together. Nations now understand that pollution, climate change, and resource problems cross borders. Traditional agreements between countries are not enough anymore. New approaches include businesses, local communities, and citizen groups working with governments. This all-hands-on-deck approach helps create better solutions for our planet. Many successful projects show that when different groups cooperate, they can solve difficult environmental problems that single countries cannot fix alone.
Environmental governance faces many challenges today. [I] Political differences between nations often slow down important decisions. [II] Some countries worry that strict environmental rules might hurt their economic growth. Despite these obstacles, new technologies are helping countries monitor environmental changes better. [III] Satellite data and computer models allow scientists to track forest loss, ocean pollution, and climate patterns. [IV] This information helps leaders make smarter decisions about protecting natural resources.
The future of environmental governance depends on innovation. Digital platforms now connect environmental experts around the world instantly. Young people are bringing fresh ideas through social media campaigns and protest movements. Indigenous communities contribute valuable traditional knowledge about sustainable living practices. Financial institutions are creating new ways to fund green projects in developing countries. These combined efforts are creating a more flexible and responsive system of global cooperation that can adapt to changing environmental conditions more quickly than old-fashioned diplomatic channels.
Effective environmental governance requires balance between global standards and local solutions. While international agreements provide important frameworks, communities need freedom to implement approaches that fit their unique situations. Successful governance models respect cultural differences while maintaining scientific standards. Education plays a crucial role in building public support for environmental policies. When citizens understand environmental issues, they make better choices and hold their leaders accountable. The most promising path forward combines strong international institutions with energetic local action to create lasting environmental solutions.
Which of the following best paraphrases the underlined sentence in paragraph 4?
Đỗ Phủ sống ở thế kỉ nào?
Read the passage carefully. Choose an option (A, B, C, or D) that best answers each question from 41 to 45.
1. It is estimated that about 40 per cent of the world's population use social media, and many of these billions of social media users look up to influencers to help them decide what to buy and what trends to follow. An influencer is a person who can influence the decisions of his or her followers because of his or her knowledge or special knowledge in a particular area, e.g. fashion, travel, or technology. Influencers are now seen by many companies as a direct way to customers' hearts. Brands are now asking powerful influencers to market their products. With some influencers charging up to $25,000 for one social media post, it is no surprise that more and more people are keen to become influencers, too. If you are one of them, then here are five tips on how to do it.
2. Choose your niche: What is the area that you know most about? What do you feel most excited talking about? Find the specific area that you are most interested in and develop it.
3. Choose your medium and write an interesting bio: Most influencers these days are bloggers and micro-bloggers. Decide which medium – such as your own online blog, Instagram or Snapchat – is the best way to connect with your followers and chat about your niche area. When you have done that, write an attention-grabbing bio that describes you and your speciality area in an interesting and unique way. Make sure that people who read your bio will want to follow you.
4. Post regularly and consistently: Many influencers post daily on their social media accounts. The more you post, the more likely people will follow you. Also, make sure that your posts are consistent and possibly follow a theme.
5. Tell an interesting story: Whether it is a photo or a comment that you are posting, use it to tell a story that will catch the attention of your followers and help them connectwith you.
6. Make sure people can easily find your content: Publicize your posts on a variety of social media by hashtags and catchy titles to make sure that they can be easily found. There is no point writing the most exciting blogposts or posting the most attractive photographs if no one is going to see them.
7. Most importantly, if you want to become a social media influencer, you need to have patience. Keep posting and your following will gradually increase. Good luck!
What is the passage mainly about?
Mỗi người dân đều có nghĩa vụ nộp thuế và được hưởng quyền lợi từ ngân sách nhà nước thông qua việc nào?
Cho dãy số \(\left(u_{n}\right)\) biết \(\left\{\begin{array}{l}u_{1}=1 \\ u_{n}=\frac{1}{3} u_{n-1}+2\end{array}\right.\). Mệnh đề nào sau đây đúng?
Cây ngô ở Cộng hòa Nam Phi được trồng tập trung ở khu nào?
Nhóm động vật nào dưới đây là động vật hoang dã
Cho bảng dữ kiện về một số thành tựu của các nền văn minh phương Đông thời cổ - trung đại.
Nền văn minh
Thành tựu
Ai Cập
Chữ tượng hình; toán học (nhất là hình học); kiến trúc và điêu khắc; kĩ thuật ướp xác; tín ngưỡng thờ đa thần.
Trung Hoa
Chữ tượng hình được viết trên mai rùa, xương thú,…; văn học (thơ Đường, tiểu thuyết Minh - Thanh); toán học (sử dụng hệ số đếm thập phân); kiến trúc và điêu khắc (Di hoa viên, Thập tam lăng,…); kĩ thuật (in, giấy, thuốc súng,…); tư tưởng, tôn giáo (Nho giáo, Đạo giáo).
Ấn Độ
Văn học (kinh Vê-đa, sử thi Ma-ha-bha-ra-ta, Ra-ma-y-a-na,…); toán học (sáng tạo số tự nhiên); tôn giáo (Bà-la-môn giáo, Hin-đu giáo, Phật giáo,…).
Một vật được thả rơi tự do. Lấy gia tốc rơi tự do là 9,8 m/s2. Hỏi trong giây thứ ba kể từ lúc được thả rơi thì vận tốc của vật đã tăng lên bao nhiêu?
Dị hóa ở vi sinh vật là quá trình như thế nào?1.html
Trong xã hội Ai Cập cổ đại không có lực lượng nào dưới đây?
Những mặt hàng nào cần phải nộp thuế bảo vệ môi trường?
Sau khi chiếm được 3 tỉnh miền Đông Nam Kỳ, thực dân Pháp gặp nhiều khó khăn trong việc tổ chức, quản lý những vùng đất mới chiếm được do
Chọn phương án đúng khi chọn khóa chính cho bảng?
Khi phân tích sơ đồ phát sinh chủng loại về một số tính trạng của các nhóm động vật có xương sống ở hình bên, nhận xét nào sau đây đúng?
Hai pin ghép nối tiếp với nhau thành bộ thì
Hình ảnh nào là đối tượng quan sát của nhân vật trữ tình trong bài thơ?
Khu vực nào có hoạt động động đất mạnh nhất nước ta?
Read the following passage about the Pathways from Today's Actions to Tomorrow's World and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
As we stand at the crossroads of environmental decision-making, the actions we take today will shape our world in 2050. Scientists warn that we're skating on thin ice with current consumption patterns and carbon emissions. Global temperatures could rise by 2-4 degrees Celsius unless significant changes occur within the next decade. Many countries have pledged to achieve carbon neutrality by 2050, but these promises require immediate implementation. Individual choices in transportation, energy usage, and consumption can collectively influence whether future generations inherit a sustainable planet or face severe climate consequences.
[I] Technological innovation represents our greatest hope for addressing environmental challenges by 2050. [II] Renewable energy sources like solar and wind are becoming increasingly affordable, potentially replacing fossil fuels entirely within thirty years. [III] Electric vehicles may dominate transportation networks, while vertical farming could transform food production in urban areas. [IV] However, these technological solutions must be developed and deployed equitably to avoid creating new disparities between wealthy and developing nations.
Social structures will undergo dramatic transformation by 2050 as demographic shifts reshape communities worldwide. Aging populations in developed countries will necessitate new approaches to healthcare, retirement, and social support systems. Meanwhile, climate migration may force millions to relocate from vulnerable coastal and drought-prone regions. Education systems must evolve to prepare our students for jobs that don't yet exist, emphasizing their adaptability and lifelong learning. Cities will need to become more resilient, incorporating green spaces and sustainable infrastructure to support growing populations.
Economic models must fundamentally change by 2050 to balance prosperity with environmental responsibility. The traditional focus on continuous growth may shift toward measuring success through wellbeing indicators rather than GDP alone. Circular economy principles will likely replace linear production models, with products designed for reuse and recycling. Resource-sharing platforms may become more prevalent, reducing individual consumption while maintaining living standards. Companies implementing genuinely sustainable practices will thrive, while those clinging to environmentally harmful methods may disappear entirely. The transition presents both challenges and opportunities for businesses willing to embrace innovation and sustainability.
The word “their” in paragraph 3 refers to _________.
Read the following passage about human life expectancy and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
In the UK, comprising England, Scotland, Wales, and Northern Ireland, jokes and tricks can be played until noon on 1 April. After midday it's considered bad luck to play a trick. Anyone who forgets this and tries a joke in the afternoon becomes an 'April Fool' themselves.
So, what kind of jokes do people play? Well, a simple example would be telling your friend that their shoelaces are undone. Then, when they bend down to do them up, you shout, 'April Fool!', and they realise their shoelaces are fine.
Maybe it's not your kind of humour, but watch out, there's always someone who will find it funny! In Ireland, a popular prank is to send someone on a 'fool's errand'. The victim is sent to deliver a letter, supposedly asking for help. When the person receives the letter, they open it, read it and tell the poor messenger that they will have to take the letter to another person. This continues and the victim ends up taking the message to several different people until someone feels sorry for them and shows them what the letter says: 'Send the fool to someone else.'
In France, Belgium, the Netherlands (or Holland), Italy and French-speaking areas of Canada and Switzerland, the 1 April tradition is known as the “April Fish”. A common joke is to try to stick a paper fish onto a victim's back without being noticed.
In which paragraph does the writer mention England and Scotland?