vectors.. theory need a bit of help?

Question

ok i knw that 2 parallel lines of the same have the same vector,,, and if the length is more or less and the line are parallel v multiply by a constant,,

my problem is,,, is a position vector the vector of that line from the origin,,,

second if there was a line of the same length and parallel to this line from the origin does it have the same vector,

Answer 1

you answered your own questions. your are correct

Answer 2

First all vectors that point in the same direction and with the same length are the same. So you can take any vector and relocate it anywhere. So the vector from (0,0) to (2,1) is the same as the vector from (-10,-10) to (-8,-9). But usually the tail is at the origin which is the most useful.

The position vector just tells in which direction is something pointing. Usually a position vector is of norm 1. For example, x is a vector which points in the direction of (1,1) but it is 8 units long. So yeah, a position is most useful when originates from the origin.

So your second guess is also correct. If there are two parallel line, you can say that the vectors are parallel but the proper way to say is that vectors are the same. So if there was a line of the same length and parallel, the vectors are the same.

Answer 3

A position vector is a vector that describes the spatial position of a point relative to a reference point called the origin.

http://en.wikipedia.org/wiki/Position_vector

This is best illustrated by way of example.

If you have a line L defined by two points on the line P and Q, you can write a vector equation for the line. Let's assume the origin is O.

L = OP + tPQ

In this equation OP is a position vector that takes you from the origin to a point P on the line. PQ is the directional vector of the line and t is a scalar that ranges over the real numbers.

Answer 4

Yes, a position vector is with respect to the origin.

Answer 5

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