Let $\displaystyle x=(5,2,4)^T$ and $\displaystyle y=(3,3,2)^T$. Compute $\displaystyle ||x-y||_1$, $\displaystyle ||x-y||_2$, and $\displaystyle ||x-y||_{\infty}$. Under which norm are the two vectors closest together? Under which norm are they farthest apart?

I computed $\displaystyle ||x-y||_1=5$ and $\displaystyle ||x-y||_2=3$. The infinity is throwing me off however. And for the distance would I just compare the square roots of the vectors?