The two sentences above are both incorrect.
In order to use these verbs correctly you must first understand their functions.
In (a): see is a non-action verb.
Seeing happens because my eyes are open.
Seeing is a physical reaction, not a planned action.
In (b): look is an action verb.
Looking at something is a planned action.
Looking happens because you want it to happen.
In ( c ): watch is also an action verb.
Like look, watching is a planned action.
You watch something because you want to.
As you can see, both look at and watch are planned actions.
So, what is the difference between looking at something and watching something?
You look at something for a short time, but you watch something for a long time.