Free vector
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Free vector is that vector whose initial point or tail is not fixed. It is also known as a non-localised vector.
For example, velocity vector of particle moving along a straight line is a free vector.
Co-initial vectors
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Co-initial vectors are those vectors which have the same initial point.
Co-terminus vectors
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Co-terminus vectors are those vectors which have a common terminal point.
Negative vector
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A vector is said to be negative of a given vector if its magnitude is the same as that of the given vector, but the direction is reversed.
Position vector
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A vector which gives the position of a point with reference to the origin of the coordinate system is called position vector.
The figure above illustrates the position vector of a particle moving in the X-Y plane. Let the particle be at P at any instant of time. Then, 
is the position vector which gives the position of the particle with reference to a fixed point in the X-Y plane. This fixed point has been chosen as the origin. Corresponding to every position of the moving particle, there is a position vector from the origin to that position of the particle. The magnitude of the position vector gives the distance of the particle from some arbitrarily chosen origin. In addition to this, the direction of the position vector gives the direction q in which P lies, as observed from 0.
It is important to note that position vectors are different for different positions of the particle.
The above explanation can be extended to a three dimensional coordinate system illustrated in figure below. In this case, the position vector is given by
