Are Vector Components Always on the X-axis and Y-axis?

[MIA6]

What's the definition of "vector components"? I mean that when I resolve a vector into two components, my teacher taught us to find its x-component which is on x-axis and y-component on y-axis, so if it be the case, then this vector must not be on either x-axis or y-axis but between. So is that the components of a vector must be on x-axis and y-axis? Or it may depends, as long as the two components are perpendicular to each other, and the vector is between them, it's okay?
Hope you can tell me, thanks.

 

[mathman]

Vectors are defined with components along mutually perpendicular axes. In the most elementary 2-d case, these are the x and y axes. However as you learn more about it, you will learn about axis rotations, where the axes are replaced by other mutually perpendicular directions.

 

[Doc Al]

I mean that when I resolve a vector into two components, my teacher taught us to find its x-component which is on x-axis and y-component on y-axis, so if it be the case, then this vector must not be on either x-axis or y-axis but between.

Why do you say that? Why can't a vector have an x or y component equal to zero?

So is that the components of a vector must be on x-axis and y-axis?

The components--by definition--are along their axes.

Or it may depends, as long as the two components are perpendicular to each other, and the vector is between them, it's okay?

The x and y components will always be perpendicular to each other--but the complete vector can point in any direction.