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Math Help - Calculus III - Vectors: point of intersection; equation of the plane

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    Calculus III - Vectors: point of intersection; equation of the plane

    I am going through a study guide and the following are stumping me:

    1.) Find the point of intersection of each of the following pairs of lines, if it exists. If a pair of lines does not intersect, indicate why not.

    x = 5t + 3, y = 2t + 1, z = t - 1
    x = 2s + 3, y = -s + 10, z = 2s - 2

    The lines do not intersect, but I must show why not. Someone please explain?



    2.) Find an equation of the plane through (8,1,3) and having a normal vector <3,5,2>


    All help would be appreciated. Thank you!
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    Re: Calculus III - Vectors: point of intersection; equation of the plane

    Quote Originally Posted by Roleparadise View Post
    1.) Find the point of intersection of each of the following pairs of lines, if it exists. If a pair of lines does not intersect, indicate why not.
    x = 5t + 3, y = 2t + 1, z = t - 1
    x = 2s + 3, y = -s + 10, z = 2s - 2

    Solve this system 5t+3=2s+3~\&~2t+1=-s+10.

    Then show the solution does not work for the z coordinate.
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