Let u= $\langle X,Y \rangle$ and v= $\langle X_1,Y_1 \rangle$. Describe the set of points $(X,Y)$ in 2-space that satisfy the stated conditions:
$(a)$ ||u - v||$=1$
$(b)$ ||u - v||$≤1$
$(c)$ ||u - v||$>1$
I don't know how to answer these questions. I see that the answer to $(a)$ would be two concentric circles where the difference between their respective radii would be 1, but I don't know how to answer the question. I am even more lost on $(b)$ and $(c)$. Any help would be appreciated. Thank you.