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Giải bài 2 trang 70 sách bài tập toán 12 - Chân trời sáng tạo

Cho (Aleft( {4; - 3;1} right)) và vectơ (overrightarrow u = left( {5;2; - 3} right)). Biểu diễn các vectơ sau đây theo các vectơ (overrightarrow i ,overrightarrow j ,overrightarrow k ). a) (overrightarrow {OA} ); b) (4overrightarrow u ).

꧋Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Cho \(A\left( {4; - 3;1} \right)\) và vectơ \(\overrightarrow u  = \left( {5;2; - 3} \right)\). Biểu diễn các vectơ sau đây theo các vectơ \(\overrightarrow i ,\overrightarrow j ,\overrightarrow k \). a) \(\overrightarrow {OA} \); b) \(4\overrightarrow u \).

Phương pháp giải - Xem chi tiết

‒ Sử dụng toạ độ của vectơ: • \(\overrightarrow {OM}  = \left( {a;b;c} \right) \Leftrightarrow M\left( {a;b;c} \right)\). • \(\overrightarrow u  = a\overrightarrow i  + b\overrightarrow j  + c\overrightarrow k  \Leftrightarrow \overrightarrow u  = \left( {a;b;c} \right)\). ‒ Sử dụng biểu thức toạ độ của phép nhân một số với một vectơ: Nếu \(\overrightarrow u  = \left( {{x_1};{y_1};{z_1}} \right)\) thì \(m\overrightarrow u  = \left( {m{x_1};m{y_1};m{z_1}} \right)\) với \(m \in \mathbb{R}\).

Lời giải chi tiết

a) \(\overrightarrow {OA}  = \left( {4; - 3;1} \right) = 4\overrightarrow i  - 3\overrightarrow j  + \overrightarrow k \). b) \(4\overrightarrow u  = \left( {20;8; - 12} \right) = 20\overrightarrow i  + 8\overrightarrow j  - 12\overrightarrow k \).

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