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If they gave us $u=(1,1)$, $v=(3,2)$, $w=(-1,0)$ and $k=5$. How do you compute $d(u,v)$? I know that $d(u,v)=\|u-v\|$ but I am lost as how to continue. Please could I get some help on this!

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What is $k$ for? Also, $w$ is not in use.

Hint: Draw it in a coordinate system on squared paper (or draw the squares yourself, or just draw a draft scheme of the situation). Then find a right triangle that fits the actual problem (with parallel sides to the coordinate axes), and finally, use the Pythagorean theorem.

In the language of inner product, what you need is: $||a||^2 = \langle a,a\rangle$.

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