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Lý thuyết Tổng và hiệu của hai vecto - SGK Toán 10 CTST

1. TỔNG CỦA HAI VECTƠ

Tổng hợp đề thi học kì 2 lớp 10 tất cả൩ các môn - Chân trời sáng tạo

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1. TỔNG CỦA HAI VECTƠ

Quy tắc ba điểm:

Với 3 điểm M, N, P ta có: \(\overrightarrow {MN}  + \overrightarrow {NP}  = \overrightarrow {MP} \)

Quy tắc hình bình hành:

Nếu OABC là hình bình hành thì ta có \(\overrightarrow {OA}  + \overrightarrow {OC}  = \overrightarrow {OB} \) 

2. TÍNH CHẤT CỦA PHÉP CỘNG CÁC VECTƠ

Phép cộng vecto có các tính chất sau:Tính chất giao hoán: \(\overrightarrow a  + \overrightarrow b  = \overrightarrow b  + \overrightarrow a \)Tính chất kết hợp: \((\overrightarrow a  + \overrightarrow b ) + \overrightarrow c  = \overrightarrow a  + (\overrightarrow b  + \overrightarrow c )\)Với mọi vecto \(\overrightarrow a ,\) ta luôn có: \(\overrightarrow a  + \overrightarrow 0  = \overrightarrow 0  + \overrightarrow a  = \overrightarrow a \)

Chú ý: \(\overrighta🌳rrow a  + ( - \overrightarrow a ) = \overright♓arrow 0 \) (Tổng hai vecto đối luôn bằng vecto-không)

 

3. HIỆU CỦA HAI VECTƠ

+) Hiệu của hai vecto \(\overrightarrow a  - \overrightarrow b  = \overrightarrow a  + \left( { - \overrightarrow b } \right)\)

Chú ý: Cho ba điểm O, A, B ta có: \(\🧜overrightarrow {🔜OB}  - \overrightarrow {OA}  = \overrightarrow {AB} \)

 

4. TÍNH CHẤT VECTƠ CỦA TRUNG ĐIỂM VÀ TRỌNG TÂM

+) M là trung điểm AB \( \Leftrightarrow \overrightarrow {MA}  🦩+ \overrightarrow {MB}  = \overrightar♏row 0 \)

+) G là trọng tâm của \(\Delta ABC\) \( \Leftrightarrow \overrightarrow {GA}  + \overrightꦬar🦩row {GB}  + \overrightarrow {GC}  = \overrightarrow 0 \)

 

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