I am trying to solve the following exercise about 3-connected graphs from this book.
(a) Show that for every two vertices $u$ and $v$ of a $3$-connected graph $G$, there exist two internally disjoint $u$-$v$ paths of different lengths in $G$.
(b) Show that the result in (a) is not true in general if $G$ is $2$-connected.
Whitney's Theorem states that a graph $G$ is $k$-connected if and only if any two vertices of $G$ are connected by at least $k$ vertex disjoint paths, so for part (a) we have that every two vertices $u$ and $v$ are connected by at least $3$ internally disjoint paths. I suppose I should use this result and try to make a proof by contradiction, but it does not work. Any hints?