Question

how do you convert the equation of a line in 3 dimensions to parametric

Answer 1

What types of equation are you starting with? Is it a vector equation or a Cartesian equation?

Answer 2

vector equations

Answer 3

So you're starting from r = (ai+bj+ck) + p(mi+nj+qk).
This can be written as
r=(a+pm)i + (b+pn)j + (c+pq)k

Hence the parametric equation would be

x=a+pm, y=b+pn, z=c+pq

Answer 4

where p would be the parameter

Answer 5

p is like the t?

Answer 6

yes

Answer 7

so you have to factor it out of the given equation then?

Answer 8

in the vector equation you usually have lambda, which I called p here. That p would become the t for the parametric form.