What are the equations for a line in 3-space passing through two given points?

[Buzzlastyear]

Homework Statement

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).

Homework Equations

Midpoint equation=( (x1+x2)/2, (y1+y2)/2, (z1+z2)/2)

The Attempt at a Solution

Midpoint of LM = (2,1,-1)

To find the direction vector I'm assuming i must find vector QLM(subscript midpoint)?

(2,1,-1) - (2,-1,3) = (0,2,-4)

Vector equation: r= (2,-1,3) + t(0,2,-4)

Parametric equations:

x=2, y=-1+2t, z=3-4t

Symmetric equations:

x=2; (y+1)/2, (z-3)/-4

x=2; (y+1)/2, (3-z)/4

Those are my answers but I'm not sure if my procedure is correct, any help is much appreciated.

 

[LCKurtz]

Your solution looks fine.