Find the parametric equation for the line through (5,1,0) that is perpendicular to the plane 2x - y + z = 1.

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Coleman Ali · Accepted Answer

r(t)=&amp;lt;5,1,0&amp;gt;+&amp;lt;2,-1,1&amp;gt;tIn parametric formx=2t+5y=1-tz=tWe are looking for when this line intersects the coordinateplanes.. In other word, we want to know where the line passesthrough the planes x = 0, y = 0, and z = 0. Starting with the intersection point for the plane z =0.   We knowthat the plane z =0 contains all points where the z coordinate is 0... Hence the z coordinate on our line must also be 0 when it intersects. Setting z = 0t=0Using t=0, in the parametric equations for x and y, we find the x and y coordinates of the intersection.x=5y=1(5,1,0)Following the same procedure for the plane y = 0, by setting y=00=1-tt=1x=7z=1(7,0,1)And for x = 0  t  =  −      5    2    y  =      7    2    z  =  −      5    2    (  0  ,      7    2    ,  −      5    2    )

Find the parametric equation for the line through (5,1,0) that is perpendicular to the plane 2x - y + z = 1.

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