Trong không gian
, cho mặt phẳng
đi qua điểm
và cắt các trục
,
,
lần lượt tại các điểm
,
,
. Viết phương trình mặt phẳng
sao cho
là trực tâm của tam giác
.
A.
![img1](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555228871_images/obj2019141476924548555228871_img1.png)
B.
![img1](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555718370_images/obj2019141476924548555718370_img1.png)
C.
![img1](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555318982_images/obj2019141476924548555318982_img1.png)
D.
![img1](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555557469_images/obj2019141476924548555557469_img1.png)
Đáp án và lời giải
Đáp án:C
Lời giải:Phân tích: Gọi
,
và
với
.
Phương trình mặt phẳng
đi qua ba điểm
,
,
là
.
Vì
nên ta có:
.
Điểm
là trực tâm của ![img13](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img13.png)
.
Ta có:
,
,
,
.
Ta có hệ phương trình: ![img19](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img19.png)
.
Phương trình mặt phẳng
là ![img22](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img22.png)
.
![img1](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img1.png)
![img2](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img2.png)
![img3](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img3.png)
![img4](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img4.png)
![img5](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img5.png)
![img6](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img6.png)
![img7](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img7.png)
![img8](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img8.png)
![img9](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img9.png)
![img10](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img10.png)
![img11](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img11.png)
![img12](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img12.png)
![img13](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img13.png)
![img14](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img14.png)
![img15](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img15.png)
![img16](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img16.png)
![img17](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img17.png)
![img18](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img18.png)
![img19](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img19.png)
![img20](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img20.png)
![img21](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img21.png)
![img22](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img22.png)
![img23](https://cungthi.online/upload/questionbank3_20201220/eduquestion/2019141476924548555/obj2019141476924548555523541_images/obj2019141476924548555523541_img23.png)