In our book of analytic geometry
we have a title The canonical form of a line
it is the equation of a line passing through a point p1(x1 , y1,z1) and parallel to a vector whose Direction Ratio is a:b:c
under another title The Symmetric (Two point) form of a line
is the equation pf line passing through the 2 points p1 (x1, y1, z1) & p2 (c2 , y2 , z2)
so what is the difference between both of them ?? I can figure out the difference between them and the parametric form but those two can't get it ???!! am so confused

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- asnaseer

I believe a line can be fixed by saying either:
1. it passes through some point and is parallel to another line, or,
2. it passes through two points in space

- asnaseer

so, if you are given just one point in space, then there would be an infinite number of lines tat you could construct passing through that point

- asnaseer

in order to /fix/ it to one particular line, you either need to say is has to be parallel to some other vector (or line), or that it also has to pass through another fixed point

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- asnaseer

do you follow?

- anonymous

I mean that either way we get the same equation why are the having two names??

- asnaseer

there are two names because they describe two different methods of getting to the equation of a line.
think of quadratic equations as an example. you can solve these by either factoring or by using the equation for the solution to a general quadratic equation. in both cases you end up with the same solutions.

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