Are all 3D directional vectors measured from the origin?

Vectors are usually given in relation to the origin. Of course, there can be many different origins since there is both a world coordinate system and various relative coordinate systems. So it really depends on which system you are using.

I don''t mean to confuse things but it might be an easier way of thinking of things... but who knows?

Here goes... A vector can be represented by two points, which in certains terms, is really a vector that is translated away from it''s origin.

So... V = <1, 1> can actually be moved to (and still have the same magnitude and direction) to V'' = <2, 2> forcing it''s origin to now be <1, 1>. So this "segment" <1, 1>-<2, 2> is now your V''.

I hope that helped if not confused you. =)

-Lewis [m80]
Play QUADz MX @
www.m80produxions.com

Exactly. That''s just translating a vector to another point and using a relative coordinate system.

Actually, a geometric vector doesn''t have an origin in itself. Rather it can be said to represent the set of all directed line segments having a specific length and direction. More generally, a vector is simply an element of a vector space.

Yeah! Maybe we can say direction and magnitude make a vector.

And we can also think in this way:

2 points detremine a vector, the start point and the end point.
If their coordinates are (xs, ys) and (xe, ye), then the vector will be (xe - xs, ye - ys). And the magnitude is:
the square root of (xe - xs)(xe - xs) + (ye - ys)(ye - ys).

Hope that will help.

quote:

---

2 points detremine a vector, the start point and the end point. If their coordinates are (xs, ys) and (xe, ye), then the vector will be (xe - xs, ye - ys). And the magnitude is:
the square root of (xe - xs)(xe - xs) + (ye - ys)(ye - ys).

---

It is, if the coordinates are given relative an orthonormal base.