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Giải bài 4.6 trang 54 SGK Toán 10 tập 1 – Kết nối tri thức

Cho bốn điểm A, B, C, D. Chứng minh rằng

☂Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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

Cho bốn điểm \(A, B, C, D\). Chứng minh rằng: a)  \(\overrightarrow {AB}  + \overrightarrow {BC}  + \overrightarrow {CD}  + \overrightarrow {DA}  = \overrightarrow 0 \) b) \(\overrightarrow {AC}  - \overrightarrow {AD}  = \overrightarrow {BC}  - \overrightarrow {BD} \)

Phương pháp giải - Xem chi tiết

Với 3 điểm A, B, C bất kì, ta có: \(\overrightarrow {AB}  + \overrightarrow {BC}  = \overrightarrow {AC} \) và \(\overrightarrow {AB}  - \overrightarrow {AC}  = \overrightarrow {CB} \)

Lời giải chi tiết

a) \(\begin{array}{l}\overrightarrow {AB}  + \overrightarrow {BC}  + \overrightarrow {CD}  + \overrightarrow {DA}  = \left( {\overrightarrow {AB}  + \overrightarrow {BC} } \right) + \left( {\overrightarrow {CD}  + \overrightarrow {DA} } \right)\\ = \overrightarrow {AC}  + \overrightarrow {CA}  = \overrightarrow {AA}  = \overrightarrow 0 .\end{array}\) b) \(\overrightarrow {AC}  - \overrightarrow {AD}  = \overrightarrow {DC} \) và \(\overrightarrow {BC}  - \overrightarrow {BD}  = \overrightarrow {DC} \) \( \Rightarrow \overrightarrow {AC}  - \overrightarrow {AD}  = \overrightarrow {BC}  - \overrightarrow {BD} .\)

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