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Math Help - Linear Algebra Lines vs. Vectors

  1. #1
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    Linear Algebra Lines vs. Vectors

    Hi, I'm new to the forum, and to linear algebra. Not having much fun with that latter, I'm afraid. So I hope that this helps me understand the concepts that it deals with.
    I guess I'll start with a question, try to work my way through it, and hopefully get it right, but if not, please correct me, and tell me where I went wrong and why.

    Find the equation of the line parallel to v=(5,-2,1) passing through the point (1,6,2), and determine whether the point (5,4,3) is on this line.

    I think that the equation of the line would be x=(1,6,2) + t (5,-2,1), because this would mean that (1,6,2) is on the line, and that the line has a direction of (5,-2,1). I'm not exactly sure how to figure out if the point is on the line, or if I'm even going in the right direction with this problem...
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  2. #2
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    Quote Originally Posted by Hellreaver View Post
    Find the equation of the line parallel to v=(5,-2,1) passing through the point (1,6,2), and determine whether the point (5,4,3) is on this line.
    I think that the equation of the line would be x=(1,6,2) + t (5,-2,1)
    You are correct!
    Now, is there a value of t for which x=(5,4,3)?
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  3. #3
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    So would it then become:

    (5,4,3)= (1,6,2) + t (5,-2,1)
    (5,4,3)-(1,6,2)=t (5,-2,1)
    (4,-2,1)= t (5,-2,1)

    and since the x values are different, and changing t from 1 to any other number would change the values of y and z, the point is not on the line?

    Edit: Wow, dumb question, of course it isn't. Alright, thanks a bunch for that. I have another one, kinda similar to the first, but I'm not sure how to go about it...

    Find parametric equations of the line that is perpendicular to the plane x+2y+3z=4 and passes through the point (1,1,-1).

    I'm not even sure where to being on this one... Should I solve for x in the equation of the plane, or what?
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