Guess what - IT IS POSSIBLE to draw three lines that are perpendicular to each other! Just imagine a globe, an equator and two perpendicular meridians. Not just possible - it's also beautiful - isn't it? :)The 'expert' hasn't heard of Spherical Geometry.
Let the rest of seven lines stay invisible.
So, all in all - DOABLE :) and the poor guy was even given a hint re. baloon..