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clumsy shark

Member

Registered: 2012-01-07

Posts: 13

Analytic Geometry

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: Analytic Geometry

hi clumsy shark

Welcome to the forum!

These are two ways to fix a line in space.

(1)  You know the line goes through a given point, and you know the direction of the line.

(2)  You know two points on the line.

From (2), we can calculate the direction of the line like this:

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob