Is there difference between a vector and a line

[dancho]

Is there difference between a vector and a line with given length and direction?

[David]

Is there difference between a vector and a line with given length and direction?

They are not the same, but are "equivalent". An actual Force is not a vector. It just has vector properties that can be represented by a directed line segment [for ease of use and solution to problems involving forces.]

[Guest]

Vector shows length + direction and Line of length shows only length..........Thanks .

[leesajohnson]

Vector shows the length and direction and if the line is given with direction and length I think it's same as vector.

[MahaVeer]

vector and a line are not the same, but are equivalent. Vector shows length + direction and Line of length shows only length.

[Guest]

Strictly speaking, a "line" doesn't have a length- a line segment does. Further, while a line has a "direction" in the sense of being, say, 30 degrees with the x-axis, a vector has a "start" point and an "end" point.

[Guest]

For example, the line segement from (0,0) to (1, 1) has two end points. There is no distinction between them.
But the vector from (0,0) to (1, 1) has "starting point" (or "tail") at (0, 0) and "end point" (or "head") at (1, 1). There is a distinction.

More abstractly (and more importantly), the vector "from (0, 0) to (1, 1)" is considered exactly the same as the vector "from (100, 100) to (101, 101)" or "from (-350, -350) to (-349, -349)". More accurately those are all "representives" of the same vector which is really the "equivalence class" of such thing.