Post by Admin on Mar 13, 2016 7:16:25 GMT
Gary
As I said in my previuos post, once we know everything about $\mathcal{K}$ other than in which direction it points, then we know everything about the new rotated $S$ other than in which direction it points, because they are in fact coincident lines, since they both pass through $p$. Then we just need to decide in which same direction they both must point. and we are home and dry.
If you find it confusing to move $p$ along $S$ before we have decided which way it points, then think of it as moving along $\mathcal{K}$ instead or just as moving along a line parallel to $\mathcal{K}$ which passes through $p$. It's all the same thing.
When I say we know everything about $S$ other than in which direction it points, I mean that we could draw it accurately on a piece of paper, but we wouldn't know at which end of it to place the arrowhead. We know the orientation of it $\pm\pi$.
Vasco
As I said in my previuos post, once we know everything about $\mathcal{K}$ other than in which direction it points, then we know everything about the new rotated $S$ other than in which direction it points, because they are in fact coincident lines, since they both pass through $p$. Then we just need to decide in which same direction they both must point. and we are home and dry.
If you find it confusing to move $p$ along $S$ before we have decided which way it points, then think of it as moving along $\mathcal{K}$ instead or just as moving along a line parallel to $\mathcal{K}$ which passes through $p$. It's all the same thing.
When I say we know everything about $S$ other than in which direction it points, I mean that we could draw it accurately on a piece of paper, but we wouldn't know at which end of it to place the arrowhead. We know the orientation of it $\pm\pi$.
Vasco
