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Giải bài 1 trang 100 sách bài tập toán 10 - Chân trời sáng tạo

Cho tam giác vuông cân ABC có AB = AC = a

🎃Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho tam giác vuông cân ABC có \(AB = AC = a\).

Tính các tích vô hướng \(\overrightarrow {AB} .\overrightarrow {AC} ,\overrightarrow {AC} .\overrightarrow {CB} \)

Lời giải chi tiết

\(\overrightarrow {AB} .\overrightarrow {AC}  = AB.AC.\cos \left( {\overrightarrow {AB} .\overrightarrow {AC} } \right) = a.a.\cos 90^\circ  = 0\)

Từ A 📖kẻ \(\overrightarrow {AD}  = \overrightarrow {CB}  \Rightarrow \widehat {CAD} = 135^\circ ;AD = BC = a\sqrt 2 \), ta có:

\(\overrightarrow {AC} .\overrightarrow {CB}  = \overrightarrow {AC} .\overrightarrow {AD}  = AC.CB.\cos \left( {\overrightarrow {AC} ,\overrightarrow {AD} } \right) = a.a\sqrt 2 .\cos 135^\circ  =  - {a^2}\)

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