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Giải bài 38 trang 92 SBT toán 10 - Cánh diều

Cho tam giác ABC vuông tại A, \(AB = 4a,AC = 5a\). Tính

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

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Đề bài

Cho tam giác ABC vuông tại A, \(AB = 4a,AC = 5a\). Tính

a)  \(\left| {\overrightarrow {AB}  - \overrightarrow {AC} } \right|\)           b) \(\left| {\overrightarrow {AB}  + \overrightarrow {AC} } \right|\)

Phương pháp giải - Xem chi tiết

Bước 1: Biến đổi hiệu/ tổng 2 vectơ tương ứng thành một vectơ có giá là các cạnh của ∆ABC

Bước 2: Tính độ dài các cạnh rồi suy ra độ dài vectơ tương ứng

Bước 3: Dựng hình chữ nhật ABDC, sử dụng quy tắc hì﷽nh bình hành để tính độ dài tổng 2 vectơ chung gốc

Lời giải chi tiết

∆ABC vuông tại A,  \(AB = 4a,AC = 5a\) \( \Rightarrow BC = \sqrt {A{B^2}ꦇ + A{C^2}}  = a\sqrt {41} \)

a) Ta có: \(\left| {\overrightarrow {AB}  - \overrightarrow {AC} } \right| = \left| {\overrightarrow {CB} } \right| = BC = a\sqrt {41} \)

b) Dựng hình chữ nhật ABCD. Khi đó \(AD = BC = a\sqrt {41} \)

Ta có: \(\left| {\overrightarrow {AB}  + \overrightarrow {AC} } \right| = \left| {\overrightarrow {AD} } \right| = AD = a\sqrt {41} \)

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