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Giải bài 4 trang 91 sách bài tập toán 10 - Chân trời sáng tạo

Cho hình thoi ABCD cạnh bằng a và có tâm O

Tổng hợp đề thi học kì 2 lớp 10 tất cả các m🐲ôn - Chân trời sáng tạo

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Đề bài

Cho hình thoi ABCD cạnh bằng a và có tâm O, góc \(\widehat {BAD} = 60^\circ \)

a) Tìm trong hình hai vectơ bằng nhau, và có độ dài bằng \(\frac{{a\sqrt 3 }}{2}\) b) Tìm trong hai hình đối nhau và có độ dài bằng \(a\sqrt 3 \)

Phương pháp giải - Xem chi tiết

Bước 1: Tìm độ dài các cạnh \(AB,BC,CD,DA,AC,BD...\) Bước 2: Xác định hướng của các vectơ có độ dài bằng \(\frac{{a\sqrt 3 }}{2};a\sqrt 3 \) Bước 3: a) Từ bước 2, chỉ ra hai vectơ cùng hướng             b) Từ bước 2, chỉ ra hai vectơ ngược hướng

Lời giải chi tiết

a) \(AB = BC = CD = DA = a\)Mặt khác \(\widehat {BAD} = 60^\circ \), suy ra tam giác ABD đều, suy ra \(BD = a,AO = \frac{{a\sqrt 3 }}{2}\)\( \Rightarrow BD = 2DO = OB = a;AC = 2AO = 2CO = a\sqrt 3 \)Suy ra các cặp vectơ bằng nhau và có độ dài bằng \(\frac{{a\sqrt 3 }}{2}\) là:\(\overrightarrow {AO} \)và \(\overrightarrow {OC} \); \(\overrightarrow {CO} \) và \(\overrightarrow {OA} \)b) Các cặp vectơ đối nhau và có độ dài bằng \(a\sqrt 3 \)là: \(\overrightarrow {AC} \)và \(\overrightarrow {CA} \)

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