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Giải bài 3 trang 97 SGK Toán 10 tập 1 – Chân trời sáng tạo

Cho hai điểm phân biệt A và B. Xác định điểm M sao cho

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

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho hai điểm phân biệt A và B. Xác định điểm M𝕴 sao cho \(\overrightarrow {MA}  + 4\overrightarrow {MB}  = \overrightarrow 0 \)

Phương pháp giải - Xem chi tiết

Bước 1: Xác định hướng của hai vectơ Bước 2: Xác định tỉ số độ dài \(\frac{{\left| {\overrightarrow {MA} } \right|}}{{\left| {\overrightarrow {MB} } \right|}}\)

Lời giải chi tiết

Cách 1:

\(\overrightarrow {MA}  + 4\overrightarrow {MB}  = \overrightarrow 0  \Leftrightarrow \overrightarrow {MA}  =  - 4\overrightarrow {MB}  \Rightarrow \frac{{MA}}{{MB}} = \frac{{\left| {\overrightarrow {MA} } \right|}}{{\left| {\overrightarrow {MB} } \right|}} = \frac{{\left| { - 4\overrightarrow {MB} } \right|}}{{\left| {\overrightarrow {MB} } \right|}} = 4\) và hai vectơ \(\overrightarrow {MA} ,\overrightarrow {MB} \) ngược hướng

Suy ra M nằm giữa AB sao cho \(\frac{{MA}}{{MB}} = 4\)

Cách 2: 

\(\begin{array}{l}
\overrightarrow {MA} + 4\overrightarrow {MB} = \vec 0\\
\Leftrightarrow \overrightarrow {MB} + \overrightarrow {BA} + 4\overrightarrow {MB} = \vec 0\\
\Leftrightarrow 5\overrightarrow {MB} = \overrightarrow {AB}
\end{array}\)

Vậy A, M, B thẳng hàng, M nằm giữa A và B sao cho \(MB = \frac{1}{5}AB\)

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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