make line render follow trajectory

hi! im trying to make a line renderer follow the trayectory of an object for a grappling hook script. the idea is to get a fixed starting point and have the line follow the curve the hook moves on and adding segments as the hook travels further. this is what i got so far grap being the gun and hook the flying rigidbody object ,

 int i =1;
 int vert =2;
 hookRenderer.setposition(0,Grap.transform.position);
 while (i<vert){
                 vert=vert+1;
                 hookRenderer.SetVertexCount(vert);
                 hookRenderer.SetPosition(i-1, lastposition);
                 hookRenderer.SetPosition(i, hookinstance.transform.position);
                 lastposition=hookinstance.transform.position;
                 i=i+1;
                 }