1. ## Parametric equation

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 the point P = (1,2,3). Find the parametric equations for the line through P which lies in the plane and is perpendicular to L.

Im lost here. I cant find an examples on how to do this problem. I have come up with this so far

x = 1 + at
y = 2 + bt
z = 3 + ct

but Im not sure that this is right.

2. Originally Posted by kenshinofkin
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 the point P = (1,2,3). Find the parametric equations for the line through P which lies in the plane and is perpendicular to L.

Im lost here. I cant find an examples on how to do this problem. I have come up with this so far

x = 1 + at
y = 2 + bt
z = 3 + ct

but Im not sure that this is right.
You are on the right track so far. A line in a plane (call it M) must be perpendicular to the plane's normal vector. We are told that the line M is also perpendicular to L. Since we know that lines lie along vectors, we can find the cross product of a normal vector of the plane and a vector pointing in the direction of line L, which will be a vector pointing in the direction of line M. You can use this to create your parametric equations and find appropriate values for a, b, and c.

3. So the normal vector for the plane would be <2,1,-1>? And I would do the cross product of <2,1,-1>X<-1,1,2>?