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Giải bài 4.22 trang 70 SGK Toán 10 – Kết nối tri thức

Tìm điều kiện của u.v để: a) u.v = |u|.|v| b) u.v = -|u|.|v|

Tổng hợp đề t🍃hi học kì 2 lớp 10 tất cả các môn - Kết nối tri ꦬthức

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

Tìm điều kiện của \(\overrightarrow u ,\;\overrightarrow v \) để: a) \(\overrightarrow u .\;\overrightarrow v  = \left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|\) b) \(\overrightarrow u .\;\overrightarrow v  =  - \left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|\)

Phương pháp giải - Xem chi tiết

Tích vô hướng \(\overrightarrow u .\;\overrightarrow v  = \left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|.\cos \left( {\overrightarrow u ,\;\overrightarrow v } \right)\)

Lời giải chi tiết

a)  Ta có: \(\overrightarrow u .\;\overrightarrow v  = \left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|.\cos \left( {\overrightarrow u ,\;\overrightarrow v } \right) = \left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|\). Khi đó \( \cos \left( {\overrightarrow u ,\;\overrightarrow v } \right) = 1\) suy ra \( \left( {\overrightarrow u ,\;\overrightarrow v } \right) = {0^o}\). Nói cách khác: \(\overrightarrow u ,\;\overrightarrow v \) cùng hướng. b) Ta có: \(\overrightarrow u .\;\overrightarrow v  = \left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|.\cos \left( {\overrightarrow u ,\;\overrightarrow v } \right) =- \left| {\overrightarrow u } \right|.\;\left| {\overrightarrow v } \right|\). Khi đó \( \cos \left( {\overrightarrow u ,\;\overrightarrow v } \right) =  - 1 \) suy ra \( \left( {\overrightarrow u ,\;\overrightarrow v } \right) = {180^o}\). Nói cách khác: \(\overrightarrow u ,\;\overrightarrow v \) ngược hướng.

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