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Giải bài 6 trang 72 SGK Toán 10 tập 2 – Cánh diều

Chứng minh khẳng định sau: Hai vectơ

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

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

Chứng minh khẳng định sau: Hai vectơ \(\overrightarrow u  = \left( {{x_1},{y_1}} \right)\), \(\overrightarrow v  = \left( {{x_2},{y_2}} \right)\) (\(\overrightarrow v  \ne 0\) ) cùng phương khi và chỉ khi có một số thực k sao cho \({x_1}{\rm{ =  }}k{x_2}\) và \({y_1} = {\rm{ }}k{y_2}\) .

Phương pháp giải - Xem chi tiết

Hai vectơ cùng phương thì tồn tại một số \(k\left( {k \in \mathbb{R}} \right)\) sao cho vectơ này bằng \(k\) lần vectơ kia.

Lời giải chi tiết

 Để hai vectơ \(\overrightarrow u  = \left( {{x_1},{y_1}} \right)\), \(\overrightarrow v  = \left( {{x_2},{y_2}} \right)\) (\(\overrightarrow v  \ne 0\) ) cùng phương thì phải tồn tại một số \(k\left( {k \in \mathbb{R}} \right)\) sao cho \(\overrightarrow u  = k.\overrightarrow v  \Leftrightarrow \left\{ \begin{array}{l}{x_1} = k{x_2}\\{y_1} = k{y_2}\end{array} \right.\) ( ĐPCM)

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

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