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Giải bài 2 trang 58 SBT toán 10 - Chân trời sáng tạo

Cho ba vectơ

๊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 ba vectơ \(\overrightarrow m  = \left( {1;1} \right),\overrightarrow n  = \left( {2;2} \right),\overrightarrow p  = \left( { - 1; - 1} \right)\). Tìm tọa độ của các vectơ a) \(\overrightarrow m  + 2\overrightarrow n  - 3\overrightarrow p \); b) \(\left( {\overrightarrow n .\overrightarrow p } \right)\overrightarrow m \)

Phương pháp giải - Xem chi tiết

Cho hai vectơ \(\overrightarrow a  = \left( {{a_1},{a_2}} \right),\overrightarrow b  = \left( {{b_1},{b_2}} \right)\), ta có: + \(\overrightarrow a  \pm \overrightarrow b  = \left( {{a_1} \pm {b_1},{a_2} \pm {b_2}} \right)\) + \(k\overrightarrow a  = \left( {k{a_1},k{a_2}} \right)\) + \(\overrightarrow a .\overrightarrow b  = {a_1}{b_1} + {a_2}{b_2}\)

Lời giải chi tiết

a) \(2\overrightarrow n  = \left( {4;4} \right),3\overrightarrow p  = \left( { - 3; - 3} \right)\)\( \Rightarrow \overrightarrow m  + 2\overrightarrow n  - 3\overrightarrow p  = \left( {1;1} \right) + \left( {4;4} \right) - \left( { - 3; - 3} \right) = \left( {8;8} \right)\)b) \(\overrightarrow n .\overrightarrow p  = 2\left( { - 1} \right) + 2\left( { - 1} \right) =  - 4 \Rightarrow \left( {\overrightarrow n .\overrightarrow p } \right)\overrightarrow m  =  - 4\left( {1;1} \right) = \left( { - 4; - 4} \right)\)

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