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What do you mean by motion in one Dimension?

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Position of any point is completely expressed by two factors : Its distance from the observer and its direction with respect to observer. That is why position is characterised by a vector known as position vector. Let point P is in a xy plane and its coordinates are (x, y). 

Then position vector (r) of point will be xi + yj and if the point P is in a space and its coordinates are (x, y, z) then position vector can be expressed as r = xi + yj + zk.

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