this one is about linear algebra.. defintion of dimension says that dimension of an object is the minimum no of coordinates needed to secify each point within it....and line is single dimensional....... we also know that in order to specify a point on line we minimum need two coordinates(x,y) how can we justify line has just oone dimension?????? i am bit confused...... hope some one can point out where am i wrong????
it is a one dimensional object in a two dimensional plane, if that makes any sense. You need to locate its start and end points in both the x and y directions. if you had a one dimensional "world" (a line) you could specify a point with only one coordinate.
Nope, a line is a one dimensional object, always. No matter what angle you view it from it only has length. It has two dimensions on an (X,Y) graph because its endpoints are not constrained to one dimension; it's a one dimensional object in a two dimensional graph, if that makes sense. There is only a one dimensional line between any two points.
In order to specify a point in a line, you need only one dimension; only one number can describe the point exactly. Think about a ruler. To describe a tickmark on a ruler you only need one number: its magnitude. Maybe what you are confused about, is that when you define a line on a 2D plane, you use two numbers x and y to describe a line on it: y=ax+b. But this time, you work in the domain of the 2 dimensions and (x,y) might as well describe any point on the plane. The extra equation actually reduces the 2 degrees of freedom to only 1. Then you come back to the 1-dimensional system. The line can still describe its points, say through the quantity "t". But in the plane, the same points need to be describe with two quantities (t , a*t+b).