I have an array of data with 3D elements. Ex: x = {{1,2,3}, {3,4,5}, {5,6,7}}.
I want to show this data in 3 dimensions, such that each point in the space is shown as a vector originating from the origin. There should be an arrow/line whose one end is at the origin $(0,0,0)$ and the other end at the point $(1,2,3)$.
Which function should I use?
For your problem, it is probably easiest to build the graphic out of graphics primitives rather than use a pre-made convenience function such as ListPointPlot3D.
This is one way to do it:
data = {{1, 2, 3}, {3, 4, 5}, {5, 6, 7}};
Graphics3D[Arrow[{{0, 0, 0}, #}] & /@ data]
I simply used the Arrow graphics primitive. I constructed a pure function that makes an arrow starting from the origin, and mapped it over the data.
I wasn't able to find a way to make ListPointPlot3D draw lines instead of points.
As an alternative to Szabolcs' Graphics3D, here is a slightly different way using ParametricPlot3D and a replacement rule.
data = {{1, 2, 3}, {3, 4, 5}, {5, 6, 7}};
ParametricPlot3D[data*u, {u, 0, 1}] /. Line -> Arrow
There are many good answers to this problem. Another is to use Arrow function:
Graphics3D[Arrow[{{0, 0, 0}, {2, 3, 4}}]], Axes -> True,
AxesLabel -> {x, y, z}]
