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Giải bài 7.43 trang 42 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho tứ diện đều ABCD, góc giữa hai đường thẳng AB và CD bằng

🐎Tổng 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 tứ diện đều ABCD, góc giữa hai đường thẳng AB và CD bằng

A. \({30^0}\).

B. \({45^0}\).

C. \({60^0}\).

D. \({90^0}\).

Phương pháp giải - Xem chi tiết

Sử dụng tích vô hướng của hai vectơ

Lời giải chi tiết

Đặt \(AB = AC = AD = a\)

\(\overrightarrow {AB} .\overrightarrow {CD}  = \overrightarrow {AB} .\left( {\overrightarrow {AD}  - \overrightarrow {AC} } \right) = \overrightarrow {AB} .\overrightarrow {AD}  - \overrightarrow {AB} .\overrightarrow {AC}  = a.a\cos {60^ \circ } - a.a\cos {60^ \circ } = 0\)

\( \Rightarrow \overrightarrow {AB}  \bot \overrightarrow {CD}  \Rightarrow \left( {\overrightarrow {AB} ,\overrightarrow {CD} } \right) = {90^ \circ } \Rightarrow \left( {AB,CD} \right) = {90^ \circ }\)

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