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Giải bài tập 7 trang 64 SGK Toán 12 tập 1 - Chân trời sáng tạo

Cho hình hộp ABCD.A′B′C′D′ có A(1; 0; 1), B(2; 1; 2), D(1; –1; 1), C′(4; 5; –5). Tìm toạ độ các đỉnh còn lại của hình hộp.

🃏Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Chân trời sáng tạo

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Đề bài

 
 
Cho hình hộp ABCD.A′B′C′D′ có A(1; 0; 1), B(2; 1; 2), D(1; –1; 1), C′(4; 5; –5). Tìm toạ độ các đỉnh còn lại của hình hộp.
 

Phương pháp giải - Xem chi tiết

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Lời giải chi tiết

Ta có: \(\overrightarrow {AB}  = (1;1;1),\overrightarrow {AD}  = (0; - 1;0)\) \(\overrightarrow {AB}  + \overrightarrow {AD}  = (1;0;1) = \overrightarrow {AC}  \Rightarrow C(2;0;2)\) \(\overrightarrow {CC'}  = (2;5; - 7)\) mà \(\overrightarrow {BB'}  = \overrightarrow {CC'}  \Rightarrow B'(4;6; - 5)\) \(\overrightarrow {A'B'}  = \overrightarrow {AB}  \Rightarrow A'(3;5; - 6)\) \(\overrightarrow {DD'}  = \overrightarrow {CC'}  \Rightarrow D'(3;4; - 6)\)
 

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