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Giải bài 2.39 trang 56 sách bài tập toán 12 - Kết nối tri thức

Trong không gian (Oxyz), cho điểm (overrightarrow a = left( {1;2;4} right)) và (overrightarrow b = left( {2;1;5} right)). Tích vô hướng (left( {overrightarrow a + overrightarrow b } right) cdot overrightarrow a ) bằng A. 54. B. -3 C. -6. D. 45.

ܫTổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

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

Trong không gian \(Oxyz\), cho điểm \(\overrightarrow a  = \left( {1;2;4} \right)\) và \(\overrightarrow b  = \left( {2;1;5} \right)\). Tích vô hướng \(\left( {\overrightarrow a  + \overrightarrow b } \right) \cdot \overrightarrow a \) bằng A. 54 B. -3  C. -6 D. 45

Phương pháp giải - Xem chi tiết

Khai triển biểu thức cần tìm sau đó áp dụng công thức tính tích vô hướng của hai vectơ và thay số.

Lời giải chi tiết

Ta có \(\left( {\overrightarrow a  + \overrightarrow b } \right) \cdot \overrightarrow a  = {\overrightarrow a ^2} + \overrightarrow a  \cdot \overrightarrow b  = {1^2} + {2^2} + {4^2} + 1 \cdot 2 + 2 \cdot 1 + 4 \cdot 5 = 45\). Vậy chọn đáp án D.

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