Phương trình tổng quát của mặt phẳng - Toán 12

1. Vecto pháp tuyến của mặt phẳng là gì?

Nếu vecto \(\overrightarrow n \ne \overrightarrow 0 \) và có giá vuông góc với \(\left( \alpha \right)\) thì \(\overrightarrow n \) được gọi là vecto pháp tuyến của \(\left( \alpha \right)\).

2. Cặp vecto chỉ phương của mặt phẳng là gì?

Nếu hai vecto \(\overrightarrow a \), \(\overrightarrow b \) không cùng phương, có giá song song hoặc nằm trong \(\left( \alpha \right)\) thì \(\overrightarrow a \), \(\overrightarrow b \) được gọi là cặp vecto chỉ phương của \(\left( \alpha \right)\).

3. Phương trình tổng quát của mặt phẳng

Trong không gian Oxyz, mỗi mặt phẳng đều có phương trình dạng Ax + By + Cz + D = 0, trong đó A, B, C không đồng thời bằng 0, được gọi là phương trình tổng quát của mặt phẳng đó. Mỗi phương trình Ax + By + Cz + D = 0 (A, B, C không đồng thời bằng 0) đều xác định một mặt phẳng nhận \(\overrightarrow n = (A;B;C)\) làm vecto pháp tuyến. Cho mặt phẳng có phương trình tổng quát là Ax + By + Cz + D = 0 . Khi đó \(N({x_0};{y_0};{z_0}) \in (\alpha ) \Leftrightarrow A{x_0} + B{y_0} + C{z_0} + D = 0\).

4. Bài tập vận dụng

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