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Решите задачу:

${(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$
${a}^{2} = { |a| }^{2}$
$|a| = \sqrt{ {4}^{2} + {( - 2)}^{2} + {( - 4)}^{2} } = \sqrt{16 + 4 + 16} = \sqrt{36} = 6 \\ { |a| }^{2} = 36$
${b}^{2} = { |b| }^{2} \\ |b| = \sqrt{ {6}^{ 2} + {( - 3)}^{2} + {2}^{2} } = \sqrt{36 + 9 + 4} = \sqrt{49} = 7 \\ { |b| }^{2} = 49$
$ab = 4 \times 6 + ( - 2) \times ( - 3) + ( - 4) \times 2 = 24 + 6 - 8 = 22 \\ \\ {(a - b)}^{2} = 36 - 2 \times 22 + 49 = 36 - 44 + 49 = 41$