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Math Help - equation of a line through a point, parallel to a plane, and perpendicular to a line

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    equation of a line through a point, parallel to a plane, and perpendicular to a line

    Q: Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane x+y+z=2 and perpendicular to the line x=1+t, y=1-t, z=2t

    I'm having trouble coming up with a sensible approach to this problem (my understanding of point/line/plane interaction is a bit shaky as solutions to similar problem have been found by applying methods used in the book examples)

    I know an equation of a line is given by \vec{r}=\vec{r_{0}}+t\vec{v} where \vec{r_{0}} is position vector of a point on the line and \vec{v} is a vector parallel with the line. The vector, \vec{n}=[1, 1, 1], is the normal vector for the parallel plane, and \vec{v}=[1, -1, 2] is the vector in the direction of the perpendicular line. Is this all I need to solve? If so, where do I go from here?
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    Re: equation of a line through a point, parallel to a plane, and perpendicular to a l

    Quote Originally Posted by sgcb View Post
    Q: Find parametric equations for the line through the point (0, 1, 2) that is parallel to the plane x+y+z=2 and perpendicular to the line x=1+t, y=1-t, z=2t
    The direction vector you need is <1,1,1>\times<1,-1,2>.
    Thanks from sgcb
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