vectors

[joecool113]

Let L be the line given by x = 2 - t , y = 1 + t, z = 1 + 2t.
L intersects the plane 2x + y - z = 1 at P = (1 , 2, 3). Find
the equations of a line through P which lies in the plane and is
perpendicular to L.

normal vector of L is n=<-1,1,2>,
if I cross <1,2,3> x <-1,1,2>= <1,-5,3>
I am not sure this is the right approach and what to do after this?

 

[pka]

Let L be the line given by x = 2 - t , y = 1 + t, z = 1 + 2t.
L intersects the plane 2x + y - z = 1 at P = (1 , 2, 3). Find
the equations of a line through P which lies in the plane and is
perpendicular to L.

The direction vector of L is \(\displaystyle <-1,1,2>\) and the normal to the plane is \(\displaystyle <2,1,-1>\).

The direction vector of the required line is \(\displaystyle <-1,1,2>\times <2,1,-1>\).