# Thread: Reflecting a line in a plane

1. ## Reflecting a line in a plane

The line l: (1,2,3)+t(3,4,5) is reflected in the plane P: 2x-2y-z+11=0
Is there any fast way of doing this? I alway first found the mirror point of (1,2,3) in P and then connected this point with the point of intersection of l and P. This is quite an easy way but unfortunately takes quite a time, it'd be grateful if somebody knew an easier way to do that!

2. That sounds to me like the simplest way and I don't think it should take all that much time.

One difficulty with that method- the line may not intersect the plane. I would, rather, find the reflections of two different points on the line, say t= 0and t= 1, and find the line through them.

3. Originally Posted by HallsofIvy
That sounds to me like the simplest way and I don't think it should take all that much time.

One difficulty with that method- the line may not intersect the plane.
It's not really such a big worry, however, because if the line does not intersect the plane you can infer that the reflected line must be parallel to the original. This information, together with the image of a single point, gives you the reflected line even in this case.