  We consider an ordinal tree $T$ on $n$ nodes, with each node assigned a
  $d$-dimensional weight vector $\pnt{w} \in \{1,2,\ldots,n\}^d,$ where $d \in
\mathbb{N}$ is a constant.
  We study path queries as generalizations of well-known {\textit{orthogonal
range queries}}, with one of the dimensions being tree topology rather than a
linear order. Since in our definitions $d$ only represents the number of
dimensions of the weight vector without taking the tree topology into account,
a path query in a tree with $d$-dimensional weight vectors generalize the
corresponding $(d+1)$-dimensional orthogonal range query.
  We solve {\textit{ancestor dominance reporting}} problem as a direct
generalization of dominance reporting problem, %in time $\O((\lg^{d-1}
n)/(\lg\lg n)^{d-2}+k)$ in time $\O(\lg^{d-1}{n}+k)$ %and space of $\O(n(\lg
n)^{d-1}/(\lg \lg n)^{d-2})$ words, and space of $\O(n\lg^{d-2}n)$ words, where
$k$ is the size of the output, for $d \geq 2.$
  We also achieve a tradeoff of $\O(n\lg^{d-2+\eps}{n})$ words of space, with
query time of $\O((\lg^{d-1} n)/(\lg\lg n)^{d-2}+k),$ for the same problem,
when $d \geq 3.$
  We solve {\textit{path successor problem}} in $\O(n\lg^{d-1}{n})$ words of
space and time $\O(\lg^{d-1+\eps}{n})$ for $d \geq 1$ and an arbitrary constant
$\eps > 0.$ We propose a solution to {\textit{path counting problem}}, with
$\O(n(\lg{n}/\lg\lg{n})^{d-1})$ words of space and $\O((\lg{n}/\lg\lg{n})^{d})$
query time, for $d \geq 1.$
  Finally, we solve {\textit{path reporting problem}} in
$\O(n\lg^{d-1+\eps}{n})$ words of space and
$\O((\lg^{d-1}{n})/(\lg\lg{n})^{d-2}+k)$ query time, for $d \geq 2.$
  These results match or nearly match the best tradeoffs of the respective
range queries. We are also the first to solve path successor even for $d = 1$.
