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[解答]
$$\displaystyle =\frac{1}{2}(\frac{1}{x+y}+\frac{1}{y+z}+\frac{1}{z+x})[(x+y)+(y+z)+(z+x)] \ge \frac{1}{2}(1+1+1)^2=\frac{9}{2}$$

$$(3,-5,7)$$及$$(-5,7,3)$$,但答案只有$$(3,-5,7)$$

[解答]
$$\vec{BA}=(-2,-1,1) , \vec{BC}=(1,2,4)\Rightarrow\vec{BD}=\vec{BA}+\vec{BC}=(-1,1,5)\Rightarrow D$$  點坐標為 $$(-1,1,5)$$ 。

$$\vec{BA}\times\vec{BC}=(-6,9,-3)=-3\cdot(2,-3,1)$$ 。而 $$\vec{DE}//\vec{BA}\times\vec{BC}$$ ，且 $$\overline{DE}=2\sqrt{14}$$  和 $$\vec{DE}\cdot(0,0,1)\geq0$$ 。

[解答]
$$\displaystyle \vec{AC}=\left(\cos\alpha-3,\sin\alpha\right), \vec{BC}=\left(\cos\alpha,\sin\alpha-3\right)$$

[ 本帖最後由 anyway13 於 2020-10-3 01:08 編輯 ]

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S=3(4,2,1)=(12,6,3), T=3(1,-2,3)=(3,-6,9)  , U=3(1,2,-1)=(3,6,-3)

ps:若是回到原題,是由(9,6,3), (3,-6,9) , (3,6,-3)所圍成的平行六面體體積

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