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Math Help - Lines in a Plane 13

  1. #1
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    Lines in a Plane 13

    Show that the points A(-9,-3,-16) and B(6,2,14) lie on the line that passes through (0,0,2) and has direction numbers (3,1,6). Describe the line segment from A to B using parametric equations with suitable restrictions on the parameter.

    I need help with the end of part B)
    Describe the line segment from A to B using parametric equations with suitable restrictions on the parameter.
    so I found the parametric equations which are:

    x=3t, y=t,z=2+6t
    But I am having trouble finding their answer of -3<=t<=2 for the restriction.

    How did they find this?

    I will add part a if it helps:
    d=AB=(15,5,30)
    d=(3,1,6)

    sym eqtn
    x/3
    y/1
    (z-2)/6

    sub in point (0,0,2)
    0=0=0 therefore point lies on line

    Ok, so how did they get the restriction on t? thanks for your help!
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  2. #2
    JML
    JML is offline
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    Quote Originally Posted by skeske1234 View Post
    But I am having trouble finding their answer of -3<=t<=2 for the restriction.

    How did they find this?
    It would appear that they have found the equation of the line by using (x,y,z) = (0,0,2) + t(3,1,6)

    In this case substituting in t=-3 gives the point A and substituting in t=2 gives the point B. Hence the segment of the line between the points A and B will be defined by using the restriction: -3<=t<=2 .
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