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Giải bài 4.43 trang 67 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Cho tam giác ABC đều, trọng tâm G, có độ dài các cạnh bằng 3

𓄧Tổng 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 tam giác \(ABC\) đều, trọng tâm \(G,\) có độ dài các cạnh bằng 3. Độ dài vectơ \(\overrightarrow {AG} \) bằng A. \(\sqrt 3 \) B. \(\frac{{3\sqrt 3 }}{2}\) C. \(\frac{{\sqrt 3 }}{2}\) D. \(2\sqrt 3 \)

Lời giải chi tiết

Gọi \(M\) là trung điểm của cạnh \(BC\)\( \Rightarrow \) \(AM = \frac{{3\sqrt 3 }}{2}\)Xét \(\Delta ABC\) đều có \(G\) là trọng tâm của tam giác\( \Rightarrow \) \(\overrightarrow {AG}  = \frac{2}{3}\overrightarrow {AM} \)\( \Rightarrow \left| {\overrightarrow {AG} } \right| = \frac{2}{3}\left| {\overrightarrow {AM} } \right| = \frac{2}{3}.\frac{{3\sqrt 3 }}{2} = \sqrt 3 \)Chọn A.

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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