# Can someone clarify and shed some light about these two statements

by jrist29
Tags: clarify, light, shed, statements
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,564 Can someone clarify and shed some light about these two statements As a very very simple example, If I set up a Cartesian coordinate system in a plane, the vector from the origin, (0, 0), to the point (1, 1) is, of course, $\vec{i}+ \vec{j}[/tex]. If I rotate that coordinate system so that my new x-axis was pointing along the line y= x (in the original coordinate system) then that [b]same[b] vector would be represented by [itex]\sqrt{2}\vec{i'}$ where, now, $\vec{i'}$ is the unit vector along the new x-axis. The components have changed, but it is still the same vector. (And, in either coordinate system, it length is "invariant".)