Parametric equation of a vector passing through a point and parallel to a line

[NewtonianAlch]

Homework Statement

Point A (1, -1, 2)

Line s = 2i - j + t(3i -j +k)

The Attempt at a Solution

Ordinarily these are pretty obvious, but in this case the line is also a parametrized vector.

So if I consider r = r0 + st

And sub in s as I would do normally, I'd end up getting t^2's, and that's not the correct answer.

The answer is r = (1, -1, 2) + t(3, -1, 1)

Which looks like the the t part of the original s line was kept with a new position vector (given point). Why is this?

 

[clamtrox]

You are given a parametric form of the line. It's of the form s = s0 + kt, where now s0 and k are vectors and t is a real number. Two lines are parallel if k1 = k2.

 

[NewtonianAlch]

"Elementary, my dear Watson"

Thanks for pointing it out!