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Câu hỏi

Góc giữa hai đường thẳng a : 3 x ​ − y + 7 = 0 và b : x − 3 y ​ − 2 = 0 là

Góc giữa hai đường thẳng  và  là

  1. 30°

  2. 90°          

  3. 60°

  4. 45°

C. Tường

Giáo viên

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Giải thích

Đường thẳng a có một vectơ pháp tuyến là 16 n 1 = 3 ; - 1 " id="_x0000_i1025" src="data:image/png;base64,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" style="width:73.5pt; "> Đường thẳng b có một vectơ pháp tuyến là 16 n 2 = 1; - 3 " id="_x0000_i1025" src="data:image/png;base64,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" style="width:74pt; "> Áp dụng công thức tính góc giữa hai đường thẳng ta có: Suy ra góc giữa hai đường thẳng bằng 30°.

Đường thẳng a có một vectơ

pháp tuyến là 

Đường thẳng b có một vectơ

pháp tuyến là 

Áp dụng công thức tính góc giữa hai đường thẳng ta có:

Suy ra góc giữa hai đường thẳng bằng 30°.

1

Câu hỏi tương tự

Cho là góc tù. Khẳng định nào sau đây là đúng?

0

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