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Giải bài 15 trang 50 sách bài tập toán 12 - Kết nối tri thức

Trong không gian Oxyz, cho điểm (Aleft( {2; - 1; - 3} right)) và mặt phẳng (left( P right):2x - 2y - z = 0) . Khoảng cách từ điểm A đến mặt phẳng (left( P right)) là A. 3. B. 6. C. (frac{2}{3}). D. (frac{1}{3}).

🐲Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Trong không gian Oxyz, cho điểm \(A\left( {2; - 1; - 3} \right)\) và mặt phẳng \(\left( P \right):2x - 2y - z = 0\) . Khoảng cách từ điểm A đến mặt phẳng \(\left( P \right)\) là

A. 3.

B. 6.

C. \(\frac{2}{3}\).

D. \(\frac{1}{3}\).

Phương pháp giải - Xem chi tiết

Ôn tập công thức tính khoảng cách từ một điểm đến một mặt phẳng trong không gian.

Lời giải chi tiết

Khoảng cách từ điểm A đến mặt phẳng \(\left( P \right)\) là \(d\left( {A,\left( P \right)} \right) = \frac{{\left| {2 \cdot 2 - 2 \cdot \left( { - 1} \right) - \left( { - 3} \right) = 0} \right|}}{{\sqrt {{2^2} + {2^2} + {1^2}} }} = \frac{9}{3} = 3\). Đáp án A.

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