Question

Determine vector, parametric and, if possible, symmetric equations for the line through Q(2, -1, 3) and the mid-point of the line segment from L(3, -2, 5) to M(1, 4, -7).

Answer 1

First find the midpoint of LM which is P(2,1,-1)
so the direction vector of PQ is [0, 2, -4] or [0,1,-2] in reduced form

so the vector equation is:
(x,y,z) = (2,-1,3) + t(0,1,-2)

You MUST know how to convert this to parametric and symmetric form.