Position Vectors | Engineering Mechanics - Civil Engineering (CE) PDF Download

Position vector 

• A straight line having one end fixed to a body and the other end attached to a moving point and used to describe the position of the point relative to the body. 
• As the point moves, the position vector will change in length or in direction or in both length and direction.
• If drawn to some scale, the change in length will signify a change in the magnitude of the vector, while a change in direction will signify a rotation of the vector.
• Changes in magnitude and direction are the only changes that a position vector can experience, and the velocity of the point is defined as the time rate of change of the position vector.
• For a point moving on a straight path, a position vector coinciding with the path is the most convenient; the velocity of the point is equal to the rate at which the magnitude of the vector changes with respect to time, and it will be a vector lying along the line. 
• For a point moving on a circular path, a position vector coinciding with a radius of the circle is the most convenient; the velocity of the point is equal to the rate at which the direction of the vector changes with respect to time, and it will be a vector at right angles to the position vector. 
• For a point moving on a noncircular curved path, the position vector changes in both magnitude and direction; the velocity of the point is the sum of the two rates of change, one a vector along the position vector and the other a vector at right angles to it.