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Math Help - parametric equations, equations of plane

  1. #1
    Junior Member
    Joined
    Oct 2008
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    parametric equations, equations of plane

    Find the parametric equations of the line through (5, -3, 4) that intersects the z-axis at a right angle.
    what do i do, since it says right angle?

    Show that the lines (x-1)/-4 = (y-2)/3 = (z-4)/-2 and (x-2)/-1 = (y-1)/1 = (z+2)/6 intersect, and find the equation of the plane that they determine.
    how would you do this??
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  2. #2
    Senior Member
    Joined
    Jul 2009
    Posts
    397
    Hi Arez

    Question 1
    You need to find the direction vector of the line that is perpendicular to z-axis.
    Any random vectors \left(\begin{array}{c}x\\y\\z\end{array}\right) will be perpendicular to z-axis if the z-component is zero. Because the line passes through (5, -3, 4), it will have direction vector \left(\begin{array}{c}5\\-3\\0\end{array}\right)

    There is other method but I think maybe this is the fastest one.


    Question 2
    Those two are Cartessian form of line equation. Have you learned how to change them to vector form of line equation?
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