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$\mathrm{Solution}:\phantom{\rule{0ex}{0ex}}\stackrel{\to }{\mathrm{p}}=2\stackrel{^}{\mathrm{i}}-4\stackrel{^}{\mathrm{j}}+7\stackrel{^}{\mathrm{k}};\phantom{\rule{0ex}{0ex}}\stackrel{\to }{\mathrm{q}}=3\stackrel{^}{\mathrm{i}}-2\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}\phantom{\rule{0ex}{0ex}}\stackrel{\to }{\mathrm{p}}×\stackrel{\to }{\mathrm{q}}\phantom{\rule{0ex}{0ex}}=\left|\begin{array}{ccc}\stackrel{^}{\mathrm{i}}& \stackrel{^}{\mathrm{j}}& \stackrel{^}{\mathrm{k}}\\ 2& -4& 7\\ 3& -2& 2\end{array}\right|\phantom{\rule{0ex}{0ex}}=\stackrel{^}{\mathrm{i}}\left(-8-\left(-14\right)\right)-\stackrel{^}{\mathrm{j}}\left(4-21\right)+\stackrel{^}{\mathrm{k}}\left(-4-\left(-12\right)\right)\phantom{\rule{0ex}{0ex}}=6\stackrel{^}{\mathrm{i}}+17\stackrel{^}{\mathrm{j}}+8\stackrel{^}{\mathrm{k}}\phantom{\rule{0ex}{0ex}}\left|\stackrel{\to }{\mathrm{p}}×\stackrel{\to }{\mathrm{q}}\right|\phantom{\rule{0ex}{0ex}}=\left|6\stackrel{^}{\mathrm{i}}+17\stackrel{^}{\mathrm{j}}+8\stackrel{^}{\mathrm{k}}\right|\phantom{\rule{0ex}{0ex}}=\sqrt{{6}^{2}+{17}^{2}+{8}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{389}\phantom{\rule{0ex}{0ex}}=19.72$

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