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Giải bài 10 trang 102 sách bài tập toán 10 - Chân trời sáng tạo

Cho tam giác ABC vuông tại A. KHẳng định nào sau đây là sai?

ওTổng 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 tam giác ABC vuông tại A. KHẳng định nào sau đây là sai?

A. \(\overrightarrow {AB} .\overrightarrow {AC}  < \overrightarrow {BA} .\overrightarrow {BC} \)  B. \(\overrightarrow {AC} .\overrightarrow {CB}  < \overrightarrow {AC} .\overrightarrow {BC} \) C. \(\overrightarrow {AB} .\overrightarrow {BC}  < \overrightarrow {CA} .\overrightarrow {CB} \)  D. \(\overrightarrow {AC} .\overrightarrow {BC}  < \overrightarrow {BC} .\overrightarrow {AB} \)

Lời giải chi tiết

 A. \(\overrightarrow {AB} .\overrightarrow {AC}  < \overrightarrow {BA} .\overrightarrow {BC} \)        + \(\overrightarrow {AB} .\overrightarrow {AC}  = 0\)         + \(\cos \left( {\overrightarrow {BA} ,\overrightarrow {BC} } \right) = \cos B > 0\) (vì \({0^ \circ } < \widehat B < {90^ \circ }\)) \( \Rightarrow \overrightarrow {BA} .\overrightarrow {BC}  > 0 = \overrightarrow {AB} .\overrightarrow {AC} \)=> A đúngB. \(\overrightarrow {AC} .\overrightarrow {CB}  < \overrightarrow {AC} .\overrightarrow {BC} \)+ \(\cos \left( {\overrightarrow {AC} ,\overrightarrow {CB} } \right) = \cos \left( {\overrightarrow {CE} ,\overrightarrow {CB} } \right) = \cos \widehat {BCE} < 0\) (vì \(\widehat {BCE} > {90^ \circ }\))+ \(\cos \left( {\overrightarrow {AC} ,\overrightarrow {BC} } \right) = \cos \left( {\overrightarrow {CE} ,\overrightarrow {CF} } \right) = \cos \widehat {ECF} > 0\) (vì \({0^ \circ } < \widehat C < {90^ \circ }\))\( \Rightarrow \overrightarrow {AC} .\overrightarrow {CB}  < 0 < \overrightarrow {AC} .\overrightarrow {BC} \) => B đúng
C. \(\overrightarrow {AB} .\overrightarrow {BC}  < \overrightarrow {CA} .\overrightarrow {CB} \)        + \(\cos \left( {\overrightarrow {AB} ,\overrightarrow {BC} } \right) = \cos \left( {\overrightarrow {BD} ,\overrightarrow {BC} } \right) = \cos \widehat {CBD} < 0\) (vì \(\widehat {CBD} > {90^ \circ }\))+ \(\cos \left( {\overrightarrow {CA} ,\overrightarrow {CB} } \right) = \cos \widehat C > 0\) (vì \({0^ \circ } < \widehat C < {90^ \circ }\))\( \Rightarrow \overrightarrow {AB} .\overrightarrow {BC}  < 0 < \overrightarrow {CA} .\overrightarrow {CB} \) => C đúngD. \(\overrightarrow {AC} .\overrightarrow {BC}  < \overrightarrow {BC} .\overrightarrow {AB} \)+ \(\cos \left( {\overrightarrow {AC} ,\overrightarrow {BC} } \right) = \cos \left( {\overrightarrow {CE} ,\overrightarrow {CF} } \right) = \cos \widehat {ECF} > 0\) (vì \({0^ \circ } < \widehat {ECF} < {90^ \circ }\))+ \(\cos \left( {\overrightarrow {BC} ,\overrightarrow {AB} } \right) = \cos \left( {\overrightarrow {BC} ,\overrightarrow {BD} } \right) = \cos \widehat {CBD} < 0\) (vì \(\widehat {CBD} > {90^ \circ }\))\( \Rightarrow \overrightarrow {AC} .\overrightarrow {BC}  > 0 > \overrightarrow {BC} .\overrightarrow {AB} \) => D đúngChọn D.

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