Problem: Sketch the coordinate curves, and the corresponding unit vector basis for the given coordinate system. Determine whether the coordinate system is orthogonal, and whether the basis vectors are constant.

1. Oblique Cartesian Coordinate System (u,v) defined by u=x and v=x+y

Question:

I'm not exactly sure how to sketch the coordinate curves. Is it simply vertical lines (corresponding to different values of u in u=x), and lines of a 45 degree angle (corrpesponding to different values of v in v=x+y)?

If someone could post what this looks like that would be helpful!

Thanks in advance