On the left you see a vector and a set of x,y axes. The divisions on the axis are one unit apart. The x,y components of the vector are printed out below.

You can rotate the axes, by clicking on the tip of the y-axis or the x-axis and moving the mouse while holding the mouse button down.

Observe how the components of change as the axes are changed, even though never changes.

You may want to verify that the magnitude (absolute value) of the vector does not change as its components are changeing by working out the equation below.