Here I am trying to delete the line shown, the curved line and straight line are two different edges of a vector image.
Hey man nothing happens when I draw, nothing is deleted at all.
If both lines are drawn and neither line is selected (or they can be selected, just easier in my opinion if not), if you use the Shaper Tool and quickly scribble over the part you want erased, it should delete it. Is that what you are doing? Not sure what you mean by nothing happens when you draw. It is already drawn.
Maybe I didn't explain my problem properly, these are two vector images, in my previous photo I was in outline view.
Solution: Shape Builder Tool.
I cannot thank you enough, appreciate the help!
My sample scenario mimics your problem. I solved this problem in my case study. Same as your drawing. Try this example.