Toán 10 tính

System32 said:

[tex]1) 4(\overrightarrow{b}-\overrightarrow{a}) + 5\overrightarrow{c}=0[/tex]
[tex]<=> 4(\overrightarrow{b}-\overrightarrow{a}) = -5\overrightarrow{c} (1)[/tex]
[tex]<=> \frac{4}{5}(\overrightarrow{a}-\overrightarrow{b}) = \overrightarrow{c} (a)[/tex]
[tex](1) <=> 16(\overrightarrow{b}-\overrightarrow{a})^2 = 25\overrightarrow{c}^2 [/tex]
[tex]<=> 16(b^2 - 2 \overrightarrow{b} \overrightarrow{a} +a^2) = 25c^2 [/tex]
[tex]<=> 16(3^2 - 2 \overrightarrow{b} \overrightarrow{a} +2^2) = 25 \times 4^2 [/tex]
[tex]<=> 16(13 - 2 \overrightarrow{b} \overrightarrow{a} ) = 400 [/tex]
[tex]<=> 13 - 2 \overrightarrow{b} \overrightarrow{a} = 25 [/tex]
[tex]<=> \overrightarrow{a} \overrightarrow{b} = 6 (b)[/tex]
[tex]2) \overrightarrow{a} \overrightarrow{b} + \overrightarrow{b} \overrightarrow{c} + \overrightarrow{c} \overrightarrow{a} [/tex]
[tex]= \overrightarrow{a} \overrightarrow{b} + \frac{4}{5}(\overrightarrow{a}-\overrightarrow{b}) \overrightarrow{b} + \frac{4}{5}(\overrightarrow{a}-\overrightarrow{b}) \overrightarrow{a} [/tex] (theo (a))
[tex]= \overrightarrow{a} \overrightarrow{b} + \frac{4}{5}(\overrightarrow{a} \overrightarrow{b} - b^2) + \frac{4}{5}(a^2 - \overrightarrow{a} \overrightarrow{b}) [/tex]
[tex]= \overrightarrow{a} \overrightarrow{b} + \frac{4}{5}(a^2-b^2) [/tex]
[tex]= 6 + \frac{4}{5}(2^2-3^2) [/tex] (theo (b))
[tex]= 6 - 4 = 2[/tex]

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