Help me understand the simple vector concept!!!(studying all alone)

As vector V, which has only x and y components, rotates from point A to B, x increases and y increases. I got this point. It's simple Cartesian coordinate analysis. But why do vector components $v_{x}$ and $v_{y}$ behave different? $v_{x}$ increases but $v_{y}$ decreases. Why? Even if they are vector components, in the end, aren't they on the same Cartesian coordinates?

I think that $v_{x}=x$ and $v_{y}=y$ Am I wrong? I think this is the point that is getting me keep confusing.

Could you explain why exactly $v_{x}$ and $v_{y}$ represent?

Solution 1:

A vector doesn't include information about the location of the arrow it represents; it only reprents the difference between the positions of the arrow's endpoints. So vectors don't "move" from one location to another, they just change direction and size.

We can draw the same vector in different places. For example, the vector $v=(0,-2)$ (with $v_x=0, v_y=-2$) might be drawn as an arrow from the point $(10,10)$ to the point $(10,8)$, or as an arrow from the point $(5,5)$ to the point $(5,3)$. It's the same vector either way.