find parametric eqns for line thru (0,1,2) parallel to....

[maeveoneill]

find parametric equations fo 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

if anyone can outline the steps to solve this.. thank you

 

[pka]

Re: find parametric equations

find parametric equations of 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

A line is parallel to a plane if the direction of the line is perpendicular to the normal of the plane: \(\displaystyle D \cdot N = 0\).
Note that (0,1,2) is on the line if t=0.

Two lines are perpendicular is their directions are perpendicular.

Thus the direction vector that you need is \(\displaystyle \left\langle {1,1,1} \right\rangle \times \left\langle {1, - 1,2} \right\rangle\).