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.
Hello, tttcomrader!
We need only the direction vector of our line,Find the parametric equation of the line through the point
that is parallel to the plane and perpendicular to the line: .
To be parallel to the plane, is perpendicular to the normal vector of the plane:
To be perpendicular to the line, is perpendicular to the vector
Hence: .
. . . Go for it!