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Giải bài 19 trang 69 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho hình lập phương (ABCD cdot A'B'C'D') có cạnh bằng (a). Góc giữa hai đường thẳng (AC) và (BC') bằng

ꦉTổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho hình lập phương \(ABCD \cdot A'B'C'D'\) có cạnh bằng \(a\). Góc giữa hai đường thẳng \(AC\) và \(BC'\) bằng

A. \({90^ \circ }\).

B. \({30^ \circ }\).

C. \({60^ \circ }\).

D. \({45^ \circ }\).

Phương pháp giải - Xem chi tiết

Phương pháp

Ta có \(AC//A'C' \Rightarrow \left( {AC,BC'} \right) = \left( {A'C',BC'} \right)\) Nhận dạng tam giác \(BA'C'\) đều \( \Rightarrow \left( {A'C',BC'} \right) = {60^ \circ }\)

Lời giải chi tiết

Ta có \(AC//A'C' \Rightarrow \left( {AC,BC'} \right) = \left( {A'C',BC'} \right)\) Xét tam giác \(BA'C'\) có ba cạnh là ba đường chéo của 3 hình vuông bằng nhau nên tam giác \(BA'C'\) đều. Vậy \(\left( {AC,BC'} \right) = \left( {A'C',BC'} \right) = {60^ \circ }\)

Chọn C

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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