Problem B. 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

L2: r = (1,1,1,) + d(0,2,3), d is in the real numbers. The new pipeline will also need to be exactly

2 units away from the point (4,0,2).

1. Determine the vector and parametric equations of L3, the line that passes through (4,0,2) and is perpendicular to L2.
2. Determine the vector and parametric equations of L1, the line that is parallel to L3 and 2 units away from (4,0,2). There will be exactly two lines that fulfill this condition.
3. Plot each line of the coordinate axes.