Problems from Product of a real number by a vector

Given the vectors $\vec{u} = (2, - 2)$ and $\vec{v} = (1, 3)$ , determine:

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$3 \vec{u} - 2 \vec{v} = 3 (2, - 2) - 2 (1, - 3) = (6, - 6) + (- 2, 6) = (4, 0)$
$- \vec{u} - \vec{v} = - (2, - 2) - (1, - 3) = (- 3, 5)$
$5 \vec{u} + 2 \vec{v} = 5 (2, - 2) + 2 (1, - 3) = (10, - 10) + (2, - 6) = (12, - 16)$
$\vec{u} + 3 \vec{v} = (2, - 2) + 3 (1, - 3) = (5, - 11)$

$\begin{array}{l} | (4, 0) | = \sqrt{4^{2} + 0^{2}} = \sqrt{16} = \sqrt{4^{2}} = 4 \\ | (- 3, 5) | = \sqrt{(- 3)^{2} + 5^{2}} = \sqrt{9 + 25} = \sqrt{3} 4 \\ | (12, - 16) | = \sqrt{12^{2} + (- 16)^{2}} = \sqrt{144 + 256} = \sqrt{400} = \sqrt{20^{2}} = 20 \\ | (5, - 11) | = \sqrt{5^{2} + (- 11)^{2}} = \sqrt{25 + 121} = \sqrt{146} \end{array}$

We can see, then, that none of these norms is one. Therefore, none of these vectors are unit vectors.

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