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

  • #1

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?
 
Last edited:

Answers and Replies

  • #2
938
9
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.
 
  • #3
"Elementary, my dear Watson"

Thanks for pointing it out!
 

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