Hi guys! I''m trying to study Linear Algebra, and at the beginning, I have a problem... I thought I know what was a vector til I started to read the math book... I would like to know why math books represent a vector as a line (?). For me, a line is represented by two points, and not by a unic one... It sound very strange for me... THank you guys! Fernando

A vector is a direction\magnitude only (can be thought of as...). A one dimensional vector(?!) is a single magnitude; a 2 dimensional vector describes the magnitudes to x and y and a three dimensional vector describes magnitudes on x y and z (etc. up to as many dimensions as you want to describe).

Thus, it doesn''t have a position in space at all.

The non-pointy end of the line is always the origin (fixed) so you can think of a vector as the point at the end of the line.

You need 2 vectors for a line not through the origin, the vector equation is v0 + lambda ( v1 - v0 )

If lambda ranges from 0 to 1 you get the segment betwixt v0 and v1.

If lambda takes any real value, you get an infinite line thru v0, v1.





[edited by - Paradigm Shifter on August 23, 2002 11:24:39 AM]

Huumm... very strange....

I''m accustomed to think vectors as single points in the space...

But, why the origin isn''t a vector too?

The origin is a vector. It''s the zero vector. It''s also the only vector which doesn''t define a "direction" and can''t be normalised.

Also, the dot product between the origin and any other vector is zero too.

Ok! But, why the origin exists? What can I do with it? I''m asking this stupid question, because it''s very strange for me! I have been programming some graphics applications that use vectors, but never had heard about that! I used to use vectors, only to represent a point on the space....

the zero vector is your global point of reference. whenever you say a point is say, for instance, (3, 4), you are saying the point is 3 units right of the origin, and 4 units up from the origin (assuming cartesian coords)

a2k

The origin is just an arbitrary reference point for a coordinate system. It''s often used as the centre of rotations for 3d models, then the models are rotated in their coord system and then translated into "world space" with a different arbitrary origin.

I''d keep studying and not worry too much about it... it''ll all make sense once you get a bit further along the road...

Ok! I''ll continue reading the book! BUt for now, I have to thank all of the guys who answered my idiots questions! It helped me a lot!!

Thank you!

A point and a vector are not exactly the same thing. But both are represented (in 3D graphics) as three real numbers, (x,y,z). The main properties of vectors are that you can add them and you can multiply them by numbers, with some reasonable properties (any takers to define a reasonable way of adding points and multiplying them by numbers?).

The concept that relates vectors and points is called "action". The action of a vector on a point is another point. You can think of this as vectors being translations of points. You can add too translations (performing one after the other), and you can multiply a translation by a number (magnifying the effect).

I haven''t written a graphics engine yet, but I would probably define two separate classes for vectors and points. The data that defines them is the same, but the operations are different. I know that most people don''t consider them separate classes, though. They are probably not very used to the concept of action of a vector space on a set of points (a.k.a. affine space). See http://mathworld.wolfram.com/AffineSpace.html