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เฉลยสำหรับข้อ 5)
$h=\frac{|\overrightarrow{r}\cdot (\overrightarrow{u}\times \overrightarrow{v}) | }{|\overrightarrow{u}\times \overrightarrow{v}|} $
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$\overrightarrow{u}\times \overrightarrow{v}$
$=(\overrightarrow{i} +\overrightarrow{j} -\overrightarrow{k})\times(\overrightarrow{i} +\overrightarrow{j} +\overrightarrow{k} )$
$=(\overrightarrow{i}) \times( \overrightarrow{i} +\overrightarrow{j} +\overrightarrow{k} )+(\overrightarrow{j} )\times (\overrightarrow{i} +\overrightarrow{j} +\overrightarrow{k})-(\overrightarrow{k} )\times (\overrightarrow{i} +\overrightarrow{j} +\overrightarrow{k} )$
$=(\overrightarrow{k} -\overrightarrow{j} )+(-\overrightarrow{k} +\overrightarrow{i}) -(\overrightarrow{j} -\overrightarrow{i} )$
$=2\overrightarrow{i}-2\overrightarrow{j} $
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$\overrightarrow{r}\cdot ( \overrightarrow{u}\times \overrightarrow{v})$
$=(2\overrightarrow{i} -3\overrightarrow{j} +4\overrightarrow{k})\cdot (2\overrightarrow{i}-2\overrightarrow{j} )$
$=(2)(2)+(-3)(-2)+(4)(0)$
$=10$
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$\therefore h=\frac{|10|}{|2\overrightarrow{i}-2\overrightarrow{j}| } =\frac{10}{\sqrt{2^{2}+(-2)^{2}} } =\frac{10}{2\sqrt{2} }=\frac{5}{\sqrt{2} }$