# Math Help - Find a parametric equation of a line

1. ## Find a parametric equation of a line

Find the parametric equation of the line through the point p = (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.

Find the parametric equation of the line through the point $P(0,1,2)$
that is parallel to the plane $x+y+z\:=\:2$ and perpendicular to the line: . $\begin{array}{ccc}x&=&1+t \\ y&=&1-t \\ z&=&2t\end{array}$
We need only the direction vector of our line, $\vec{v}$

To be parallel to the plane, $\vec{v}$ is perpendicular to the normal vector of the plane: $\vec{n} \:=\:\langle 1,1,1\rangle$

To be perpendicular to the line, $\vec{v}$ is perpendicular to the vector $\vec{u} \:=\:\langle 1,\,-1,\,2\rangle$

Hence: . $\vec{v} \;=\;\vec{n} \times \vec{u}$

. . . Go for it!