how do you represent a vector that starts somewhere other than the origin?
fuck wrong pic
>>7724883
As one that starts at the origin
You should always think of vectors as starting from the origin and just encoding direction and magnitude, it really doesn't matter where their startpoint is
Even like normal vectors to planes or a velocity vector of a particle
A vector doesn't start anywhere.
>>7724887
> it really doesn't matter where their startpoint is
then why do 3d vectors exist? the third parameter is just to encode the starting point
I think the OP is thinking about vectors in affine spaces: https://en.wikipedia.org/wiki/Affine_space
>>7724901
Um... No.
The third parameter encodes the magnitude along the z axis.
>>7724944
no, the third parameter is whatever I want it to be for my own use
>>7724948
Ok then, assume you use the third parameter to encode the starting position of the vector in a 2D space. But you can't, as you need two values to define a point in 2D space, thus you either have to use a 4th parameter, or reduce the vector to a scaler.
>>7724955
yeah thats what I meant
how do I do it now
Vectors are independent of a coordinate system.
>>7724939
that's what I wanted thanks
>>7724883
At any point p in say, R^2, you can consider the tangent space of that point which is itself a vector space. It is essentially another copy of R^2 but just centered at the point p. Any vector that eminates from a point p would live in the tangent space of p.
(Source: Spivak's Calculus on Manifolds)
