Question

find the equation of the line joining the points (-7,6,-3) and (7,-6,-3).

Answer 1

let  we will take A and B as
   A(-7,6,3) &  B(7,-6,3)
 by taking parametric representation for the line AB
then consider T as a real valued parameter

 x = x1 + (x2 - x1) t =  -7 + 14 t
  y = y1 + (y2 - y1) t =  6 -12 t
  z = z1 + (z2 - z1) t  =  3 - 6 t

Answer 2

let the given points be
 -7i+6j -3k
and  7i -6j-3k
vector equation of the straight lines joining A(a) and B(b) is r = (1-t)a +tb
 the equation of the line joining the points (-7,6,-3) and (7,-6,-3) is
r = (1-t)(-7i+6j -3k) + t(7i -6j-3k)