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Yes, as displacement is the shortest distance which can be from any path.
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Say there are three points A, B and C


Your parents told you to go to 'B' via 'C'
You travelled from A to C and then C to B.

So which is your original position? that is 'A' and
Which is your Final position ? that is 'B'

So from where you have been displaced from Point 'A' to Point 'B'.

So your DISPLACEMENT has been occured from A to B. When you are talking of your Displacement at Point 'B' you are talking in a direction from Point 'A' to
continuing above -
Point 'B'. But you are not talking of the Point 'C'. So your Displacement is independent of the Point 'C'.

So your Displacement will be the Straight line Distance From A to B and it will be with an arrow indicating the DIRECTION from A to B.Hence dispancement is a Vector Quantity.

But in case of DISTANCE .

Total Distance covered by you from A to B = Distance from A to C +Distance from C to B
Yes displacemnt is independent of path...like displacemt on triangular path will be hypotenuse..on circular it will be diameter,,,so it doesnot depend on path..

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Displacement is defined as the shortest distance from mean position to other extreme position 
so if u are going on a rectangular path 
u might go along the sides from one opposite CORNER to other 
u might go diagonally 

in both the cases displacement is equal to the length of diagonal[as it is the shortest path] 

hence proved that it is independent of path
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