Question 609265
As your definition says, if AB is a zero vector then A and B are the same point.

Think about this graphically. Say point A is (3,3). Then B is also (3,3). There is no distance between these two points (because they are the same point.)
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The there no displacement is the x-direction or the y-direction. So, the components of the zero vector are all zero. In 2-dimensional algebra, you sometimes see it written like this 
vector AB = <0,0>. 
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I hope this helps. This is very simple, but sometimes the simplest things seem confusing when you are getting started.
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Feel free to email if you still have questions.
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Ms.Figgy
math.in.the.vortex@gmail.com