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Giải bài tập 2.27 trang 73 SGK Toán 12 tập 1 - Kết nối tri thức

Cho hình hộp ABCD.A’B’C’D’. Khẳng định nào dưới đây là sai? A. \(\overrightarrow {AB} + \overrightarrow {CC'} = \overrightarrow {AB'} \). B. \(\overrightarrow {AB} + \overrightarrow {AD} + \overrightarrow {AA'} = \overrightarrow {AC'} \). C. \(\overrightarrow {AD} + \overrightarrow {BB'} = \overrightarrow {AD'} \). D. \(\overrightarrow {AB} + \overrightarrow {CC'} = \overrightarrow {AC'} \).

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

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

Cho hình hộp ABCD.A’B’C’D’. Khẳng định nào dưới đây là sai?
A. \(\overrightarrow {AB} + \overrightarrow {CC'} = \overrightarrow {AB'} \).
B. \(\overrightarrow {AB} + \overrightarrow {AD} + \overrightarrow {AA'} = \overrightarrow {AC'} \).
C. \(\overrightarrow {AD} + \overrightarrow {BB'} = \overrightarrow {AD'} \).
D. \(\overrightarrow {AB} + \overrightarrow {CC'} = \overrightarro💃w {AC'} \).

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về quy tắc hình hộp để tìm câu đúng: Cho hình hộp ABCD.A’B’C’D’. Khi đó, ta có: \(\overrightarrow {AB}  + \overrightarrow {AD}  + \overrightarrow {AA'}  = \overrightarrow {AC'} \) Sử dụng kiến thức về hai vectơ bằng nhau để tìm câu đúng: Hai vectơ \(\overrightarrow a \) và \(\overrightarrow b \) được gọi là bằng nhau, kí hiệu \(\overrightarrow a  = \overrightarrow b \), nếu chúng có cùng độ dài và cùng hướng. Sử dụng kiến thức về quy tắc ba điểm để chứng minh: Nếu A, B, C là ba điểm bất kì thì \(\overrightarrow {AB}  + \overrightarrow {BC}  = \overrightarrow {AC} \).

Lời giải chi tiết

Vì ABCD là hình bình hành nên \(\overrightarrow {AB}  = \overrightarrow {DC} \). Vì DC’B’A là hình bình hành nên \(\overrightarrow {DC'}  = \overrightarrow {AB'} \) Do đó, \(\overrightarrow {AB}  + \overrightarrow {CC'}  = \overrightarrow {DC}  + \overrightarrow {CC'}  = \overrightarrow {DC'}  = \overrightarrow {AB'} \) nên A đúng, D sai. Vì ABCD.A’B’C’D’ là hình hộp nên \(\overrightarrow {AB}  + \overrightarrow {AD}  + \overrightarrow {AA'}  = \overrightarrow {AC'} \) (quy tắc hình hộp) nên B đúng. Ta có: \(\overrightarrow {AD}  + \overrightarrow {BB'}  = \overrightarrow {AD}  + \overrightarrow {DD'}  = \overrightarrow {AD'} \), do đó C đúng Chọn D

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