How to generate vector arrows that conforms to a raster slope layer?
This is for display/mapping purposes only? Use a DEM or TIN and display your arrow lines in ArcScene.
EDIT: given your update about your data and software not working-
Try this:
1) Make a raster surface covering the extent of your data with a cell size of 100m (or smaller or larger if that doesn't suit)
2) Convert that raster to a polygon layer e.g. 'area_grid100m'
3) Do a spatial join and assign all points a polygon cell id from one of the unique id fields in 'area_grid100m'
4) Use Summarize to get the mean lat/long of the start points and mean lat/long of the end points for each polygon. Summarize on the polygon id field and get select mean for both the lat and long fields
5) Add summary table to ArcMap, right click and select Display XY Data (set X Field as longitude and y Field as latitude). Right right the result and select Data > Export Data to make it permanent. You will now have two points per 'area_grid100m' cell.
5) Recreate your lines using this new file, which will give you one line per cell
If the res is not small enough, make the 'area_grid' cells smaller.
I would like to generate vector arrows that conform to the topography/slope of a raster dataset of a river catchment area. 
I have created a Fishnet grid of points in ArcGIS and I would like to create a single arrow for each point of a set length that will follow the shape of the slope i.e. follow the path of least resistance, the line will follow progressively small numbers in a 3 x 3 grid.
I think I can generate the vector arrows using vector plot. Is it possible to achieve the lines conforming to the raster?
UPDATE: I have ~200,000 lines that I generated from a grid of points. I am going to turn these into a raster using R and set it to the same resolution as my slope raster. 
Any ideas on how to layer the raster lines on the slope so I can get the lines to follow the lowest values of the slope?