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Giải bài tập 4 trang 64 SGK Toán 12 tập 1 - Cánh diều

Cho hình hộp ABCD.A’B’C’D’. Gọi G là trọng tâm tam giác AB’D’.Chứng minh rằng \(\overrightarrow {A'C} = 3\overrightarrow {A'G} \)

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Đề bài

 
 
Cho hình hộp ABCD.A’B’C’D’. Gọi G là trọng tâm tam giác AB’D’.Chứng minh rằng \(\overrightarrow {A'C}  = 3\overrightarrow {A'G} \)
 

Phương pháp giải - Xem chi tiết

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Lời giải chi tiết

G là trọng tâm của tam giác AB’D’ => \(3\overrightarrow {A'G}  = \overrightarrow {A'A}  + \overrightarrow {A'B'}  + \overrightarrow {A'D'} \)( tính chất trọng tâm) Có \(\overrightarrow {A'A}  + \overrightarrow {A'B'}  + \overrightarrow {A'D'}  = \overrightarrow {A'C} \)( quy tắc tình hợp) =>\(\overrightarrow {A'C}  = 3\overrightarrow {A'G} \)
 

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