Thank you Bart for your answer.

I used part of your solution. This is what I did:

            split = new OpenLayers.Control.Split({
                layer: vectors,
                source: vectors,
                tolerance: 0.0001,
                eventListeners: {
                    beforesplit: function(event) {
                                                var x1, x2, y1, y2;
                                                x1 = 
event.source.geometry.components[0].x;
                                                y1 = 
event.source.geometry.components[0].y;
                                                x2 = 
event.source.geometry.components[1].x;
                                                y2 = 
event.source.geometry.components[1].y;
                                                var target = {x1: x1, y1: y1, 
x2: x2, y2: y2};
                                                //alert(x1,y1,x2,y2);
                                                var splitResult = 
event.target.geometry.splitWithSegment(target);
                                                var point = 
splitResult.points[0];
                                                var featureToAdd = new 
OpenLayers.Feature.Vector(point);
                                                
points.addFeatures(featureToAdd);
                    }
                }
            });

I used the source property to get the coordinates of each point. After, I
used the splitWithSegment() function because it returns the intersection
points.

Maxime
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