I'm using Corel Draw X6. I have drawn a vector curve facing to the left. When I rotate it to the right, reangle and resize, it becomes jagged. How can I fix this.
If you are making a path and stroking a line on it, this is more likely a raster line which then suffers from scaling as you observed. Unfortunately, vector images cannot totally eliminate aliasing, since aliasing is a byproduct of rendering a vector image to the screen.
With vector art that is purely curves with no raster textures nor effects, the art is stored as "the math" used to create the curves and lines. What this means is that there is no aliasing present in the drawing itself until it is rendered to the screen, printer, or printing plate. The drawing is an idealized description.
When rendered there is usually a square grid and on the screen this is a square grid of pixels. Aliasing happens when the grid is too course to describe a curve smoothly. The solution to this is to make the grid finer. This means increasing the number of pixels in the same area. The aliasing never goes away, but it becomes smaller. On a normal printed page, the aliasing is small enough that it is indistinguishable at arms length.
Obviously, the pixel grid of a screen is fixed and cannot be made smaller, but vectors still benefit from the ability to scale them up for e.g. dynamic websites. Raster images lose quality when scaling up because you are scaling up already-rendered aliasing.