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Homework Help: Vector lines

  1. Oct 5, 2011 #1
    Am I doing this right?

    1. The problem statement, all variables and given/known data
    A.) Find the parametric equation for the line [itex]\overline{L}[/itex] through (2,-1,4) and perpendicular to the lines:
    [itex]\overline{r_{1}}[/itex](t) = <1,2,0> + t<1,-1,3>
    [itex]\overline{r_{2}}[/itex](s) = <0,3,4> + s<4,1,-2>

    B.) Determine the point of intersection of the line and the plane 2x+2y-3z = 12

    2. Relevant equations

    3. The attempt at a solution
    Part A
    [itex]\overline{r_{1}}[/itex]X[itex]\overline{r_{2}}[/itex] = -1[itex]\overline{i}[/itex] + 14[itex]\overline{j}[/itex] + 5[itex]\overline{k}[/itex]
    [itex]\overline{L}[/itex](t) = <2,-1,4> + t<-1,14,5>

    so in parametric form:
    x = 2-t
    y = -1+14t
    z = 4+5t

    I'm kinda confused because one is with respect to "t" while the other is with respect to "s." Does it matter? I haven't done Part B yet because I want to make sure the first part is good first.

    Any help is greatly appreciated!
  2. jcsd
  3. Oct 5, 2011 #2
    No it doesn't matter what the parameter is. It's probably better that they are different
  4. Oct 5, 2011 #3


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    Staff Emeritus
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    Yes, your result looks good.

    I would write the parametric form of the line as an ordered triple. Maybe just a matter of taste.
  5. Oct 5, 2011 #4
    Thanks guys! =)
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