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Giải bài 4 trang 82 SGK Toán 10 tập 1 – Cánh diều

Cho hình vuông ABCD có độ dài cạnh bằng 3cm. Tính độ dài của các vectơ AB, AC

🐓Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

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Đề bài

Cho hình vuông ABCD có độ dài cạnh bằng 3cm. Tính độ dài của các vectơ \(\overrightarrow {AB} ,\overrightarrow {AC} \).

Phương pháp giải - Xem chi tiết

+) Độ dài của vectơ \(\overrightarrow {AB} \) là độ dài đoạn thẳng AB. Bước 1: Xác định độ dài của vectơ \(\overrightarrow {AB} ,\overrightarrow {AC} \). Bước 2: Tính các cạnh đó dựa vào cạnh hình vuông.

Lời giải chi tiết

 

Ta có: \(|\overrightarrow {AB} | = AB\) và \(|\overrightarrow {AC} |\; = AC.\)Mà \(AB = 3,\;AC = \sqrt {A{B^2} + B{C^2}}  = \sqrt {{3^2} + {3^2}}  = 3\sqrt 2  \)\( \Rightarrow \;|\overrightarrow {AB} |\, = 3;\;\;|\overrightarrow {AC} |\, = 3\sqrt 2 \)

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