1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: How to find which of three points are on a line?

  1. Sep 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Which of these three points falls on the line?

    l: r(t)=(i+2j)+t(6i+j-5k)

    P(1,2,0); Q(-5,1,5); R(-4,2,5)

    I have the answer, but I don't understand why P and Q fall on the line but R does not. Is it because the i and j magnitudes are different for R?

    2. Relevant equations

    3. The attempt at a solution

    (1+6t) = 1








  2. jcsd
  3. Sep 13, 2013 #2
    First, you are right that P and Q fall on the line and R does not. And as you see, R is not on the line because using those points you get 3 incompatible equations in t.

    Whether a point falls on a line depends on all 3 magnitudes, i, j and k, and the trivial answer to your question is that most combinations will not work i.e. most 3 dimensional points are not on any given line.

    However, working backwards from the equation we can get some insight. For example r(0) = i + 2j. So the point that fits there is P = (1,2,0). When you look at r(-1) = -5i + j - 5k, you see that Q = (-5,1,-5) is a point on the line.

    But your incompatible equation for R tells you that there is no possible t for which r(t) = R. It's not really deeper than that.
  4. Sep 13, 2013 #3
    Thanks! I think I understand, but what about the t=0 in R? Does this value not count since there is already an incompatible value in its components?
  5. Sep 14, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The line has parametric equations x = 1 + 6t, y = 2 + t, z = -5t. A point (a,b,c) lies on the line if the equations a = 1+6t, b = 2+t, c = -5t are compatible; that is, we must get the same t from all three equations.
  6. Sep 14, 2013 #5
    Thanks a bunch! That's what I needed.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted