Question

what is line of equation in 3d space?

Answer 1

I think the most intuitive form is a parametric equation:

(x,y,z) = (a,b,c)t + (p,q,r),
t ranges over the real number. The vectors (a,b,c) and (p,q,r) are constant.

The vector (a,b,c) tells you in what direction the line is going.

Answer 2

*real numbers

Answer 3

A line in 3D is the intersection of two planes, so it can be expressed that way, too. JamesJ is correct. You can also go to http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfLines.aspx to see other ways and get an explanation.