A pipeline engineer needs to find the line that will allow a new pipeline to intersect and join an existing pipeline at a right angle. The existing line has a pathway determined by the equation The new pipeline will also need to be exactly 2 units away from the point (4, 0, 2).

Determine the vector and parametric equations of L3 the line that passes through (4, 0, 2) and is perpendicular to L2.