Question

Let L1 be the line passing through the points Q1=(−3, −1, 5) and Q2=(−1, −7, −1) and let L2 be the line passing through the point P1=(3, −17, −9) with direction vector →d=[−1, 1, −1]T. Determine whether L1 and L2 intersect. If so, find the point of intersection Q. If not, find a value for the z-coordinate of P1 so the resulting lines do intersect.

Answer 1

I've got the first part of the question, however I can't figure out how to find the value of the z-coordinate for P1 so the lines do intersect