Proving geometric theorems by vector method

I am learning vectors in which there is a section in which geometric theorems are proved with the help of vectors. However while solving problems I often face difficulty on how to proceed ,where to use dot product, cross and etc.Is there any systematic manner on how to prove these ? Please help.:frown:
 
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Why don't you give us some examples of problems you've had trouble with, and tell us how you've tried to approach them so far, and we'll see if we can help.
 

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