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Giải bài 7 trang 87 SGK Toán 10 tập 1 – Cánh diều

Cho hình vuông ABCD có cạnh a. Tính độ dài các vecto sau:

𒀰Tổng 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 cạnh a. Tính độ dài các vecto sau: a) \(\overrightarrow {DA}  + \overrightarrow {DC} \) b) \(\overrightarrow {AB}  - \overrightarrow {AD} \) c) \(\overrightarrow {OA}  + \overrightarrow {OB} \) với O là giao điểm của AC và BD.

Phương pháp giải - Xem chi tiết

Xác định vecto tổng (hiệu) rồi tính độ dài.

Lời giải chi tiết

 

a) Do ABCD cũng là một hình bình hành nên \(\overrightarrow {DA}  + \overrightarrow {DC}  = \overrightarrow {DB} \)\( \Rightarrow \;|\overrightarrow {DA}  + \overrightarrow {DC} |\; = \;|\overrightarrow {DB} |\; = DB = a\sqrt 2 \)b) Ta có: \(\overrightarrow {AD}  + \overrightarrow {DB}  = \overrightarrow {AB} \) \( \Rightarrow \overrightarrow {AB}  - \overrightarrow {AD}  = \overrightarrow {DB} \)\( \Rightarrow \left| {\overrightarrow {AB}  - \overrightarrow {AD} } \right| = \left| {\overrightarrow {DB} } \right| = DB = a\sqrt 2 \)c) Ta có: \(\overrightarrow {DO}  = \overrightarrow {OB} \)\( \Rightarrow \overrightarrow {OA}  + \overrightarrow {OB}  = \overrightarrow {OA}  + \overrightarrow {DO}  = \overrightarrow {DO}  + \overrightarrow {OA}  = \overrightarrow {DA} \)\( \Rightarrow \left| {\overrightarrow {OA}  + \overrightarrow {OB} } \right| = \left| {\overrightarrow {DA} } \right| = DA = a.\) 

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