Tỉ số OA OB

Clarifying point locations

I’m mapping out triangle ABC's vertices: A on ray Ox and B on ray Oy, with O as the origin. This setup clarifies the coordinates and their relationship for further analysis.

Evaluating perpendicularity

I'm examining B as (-a, b, 0) and C as (-a, -b, z_C). Their orthogonality reveals specific insights into the triangle configuration and coordinates.

Thought about tỷ số OA/OB cho 4 giây

Giả sử hệ trục tọa độ $Oxyz$ với $O$ là gốc tọa độ. Theo giả thiết:

• Tam giác $ABC$ vuông tại $A$.
• Điểm $A$ nằm trên tia $Ox$, nên ta có tọa độ $A = (a,0,0)$ với $a > 0$.
• Điểm $B$ nằm trên tia $Oy$, nên $B = (0,b,0)$ với $b > 0$.
• Trọng tâm $G$ của tam giác $ABC$ thuộc tia $Oz$, nghĩa là tọa độ của $G$ có dạng $(0,0,z_G)$ với $z_G > 0$.

Vì $G$ là trọng tâm nên:

Thay tọa độ ta có:

Do $G$ nằm trên $Oz$, nên hoành độ và tung độ của $G$ bằng 0:

Vậy $C = (-a,-b,z_C)$ với $z_C$ là một số thực chưa xác định.

Tiếp theo, tam giác $ABC$ vuông tại $A$ nên:

Tính các véc-tơ:

Tích vô hướng:

Điều kiện vuông tại $A$ cho ta:

Cuối cùng, độ dài $OA = a$ và $OB = b = a\sqrt2$.

Tỉ số cần tìm:

Suy nghĩ cho 1 giây

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Suy nghĩ cho trong giây lát

Benefits and Drawbacks of Household Robots

Household robots offer numerous advantages that enhance daily life. They automate tasks like cleaning, cooking, and lawn care, saving time and allowing people to focus on more important activities. Smart robots can perform tasks consistently and efficiently, reducing errors. For families with elderly members or individuals with disabilities, these robots provide essential assistance, promoting independence and safety.

However, there are also disadvantages to consider. The initial cost of purchasing and maintaining household robots can be high, making them inaccessible for some families. Operating these devices may require technical knowledge, which can be a barrier for some users. Privacy concerns arise as robots often collect data and connect to the internet, posing potential security risks. Additionally, excessive reliance on robots for daily tasks might reduce physical activity and human interaction, potentially impacting health and social skills.

In summary, while household robots offer significant benefits in terms of efficiency and support, it is important to address the costs, privacy issues, and possible effects on human behavior to ensure their effective integration into homes.