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Giải bài tập 5.3 trang 51 SGK Toán 12 tập 2 - Cùng khám phá

Viết phương trình mặt phẳng trung trực của đoạn thẳng AB với \(A(2;3; - 4)\) và \(B(4; - 1;0)\).
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Đề bài

Viết phương trình mặt phẳng trung trực của đoạn thẳng AB với \(A(2;3; - 4)\) và \(B(4; - 1;0)\).

Phương pháp giải - Xem chi tiết

- Trung điểm \(I\) của đoạn thẳng AB là: \(I\left( {\frac{{{x_A} + {x_B}}}{2},\frac{{{y_A} + {y_B}}}{2},\frac{{{z_A} + {z_B}}}{2}} \right)\) - Vectơ pháp tuyến của mặt phẳng trung trực là vectơ \(\overrightarrow {AB} \).

Lời giải chi tiết

- Trung điểm \(I\left( {\frac{{2 + 4}}{2};\frac{{3 - 1}}{2};\frac{{ - 4 + 0}}{2}} \right) = (3;1; - 2)\). - Vectơ pháp tuyến \(\overrightarrow {AB}  = (4 - 2; - 1 - 3;0 + 4) = (2; - 4;4)\). - Phương trình mặt phẳng: \(2(x - 3) - 4(y - 1) + 4(z + 2) = 0\) Rút gọn: \(x - 2y + 2z + 3 = 0\)

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