Find the intersection of two planes with the traces that are cut out of the drawing. If we follow the procedure of intersection of planes, we observe that the traces of the planes, are not cut in the space of the drawing. For this reason, we use the auxiliary drawing method.
That is to draw a plane, for example, a horizontal, by the dimension that we want. In this case, having neither of the two traces of the line of intersection, we must draw two horizontal planes, to be able to find two points of this line. In the intersections of the Delta plane, with Alpha and beta, we obtain the point A. and in the intersections of the plane Pí, with the two dice, we will have another point B. The Union of these two points, generates the wanted line.
Extension of the traces, out of the drawing, to check the solution. We draw two horizontal auxiliary planes, by the dimensions or heights that we want. then trace the intersections of the Alpha plane, with the two auxiliary planes. The horizontal projections of these lines will be parallel to the Alpha one trace. Later, we found the intersections of the beta plane, with the auxiliary planes. Its horizontal projections will be parallel to the beta one trace. At the point of cut of the intersection lines of the Delta Auxiliary plane, with the two dice, we will find the point A, common to these three planes. We climbed the point to the Delta two trace, to draw its vertical projection.
We repeat the same procedure with the auxiliary plane pí. and therefore, the point of cut of the lines of intersection of this auxiliary plane, with the two dice, will be found the point B, common to these three planes. We raised the point to the trace Pí two, to draw its vertical projection. We join the projections A one with B one, to draw the projection I one of the intersection line. uniting the projections A two with B two, we will draw the projection I two of the intersection line. prolonging I two over the ground line, we will get the projection H two of the searched straight.
Then we also prolong the one on the ground line, finding the projection v one, of this straight. We check that the traces v two and H one, are outside the drawing.