The same formula is suitable
I'm not in school, and I'm not looking for any answer to any homework assignment. I have something I'm doing on my own, and I wanted to see if anyone comes up with the same formula, or close to it, as I did for the following.
Take a graph: draw a line so that , which we know is a angle and a angle from heading in a positive and negative direction on to infinity.
Now, let's say that the line goes to then then etc. What formula would also extend the line to ...ect., as the line extends positively?
In other words, you start from and the vectors extend positively, and negatively in proportion to each other. When the vector goes from to to it then extends to at the same time to , , etc.
I understand people have their own work and may not want to be sidetracked with this, but I do appreciate anything anyone has to suggest. My guess is this is a well-known formula, and I'm just don't know well enough to know it. Nevertheless, I want to get this simple formula down before proceeding on with my work.
Thank you very much in advance for anything.
Thank you, I thought about that, that simply X=Y would do, but that produces an infinite line in both directions. I was looking for a formula, or call it a model, if you will, that indicats that as the line goes to 1,1 it also goes to -1,-1. I have a formula I'd like to show here, but I'm not sure how, just yet. But I will try using TEX, and do a bunch of edits and see what happens. Here it goes:
OK, above is the formula I have come up with.
Jeez...talk about a crash course in LaTex
In your opinion, what is wrong with this formula? does it do what I am wanting it to do?
I don't know. I think I don't need the summation symbols. I'm not summing an infinite series for (x,y). I'm just trying to say that if (x,y) is such and such a coordinate, then the line moves from zero as well to the negative of that coordinate.
I should have waited to post this until I worked with it. Oh well, it was good LaTex practice.
Again, I realize this takes up your time, so any comments I appreciate.
Thanks for the input, and now I wish I had waited before posting about this until I worked it out better. Nevertheless, I know what means, or at least what it looks like. It's a line that runs infinitely in both directions from , i.e.,
What I want to show is that there is a force starting at point . If the force increases in magnitude in one direction, there is a corresponding increase in the other direction. Thus if the increase in magnatude is represented by a line going from to in the first quadrant of the graph, the line also increases in the third quadrant of the graph from to .
is not the formula that illustrates this, or at least it doesn't seem that way to me. Because as has been pointed out, or other forms of saying the same thing such as merely stand for a line that goes from infinity to infinity along that vector.
this is all very confusing. Why are you trying to find an equation to draw 2 vectors at once?
If your objection to y=x is that it is unbounded, then you can simply add a boundary
Alternatively, graph the vectors seperately:
Vector 1: (c,c)
Vector 2: -(c,c)