In the realm of Kinematics, understanding the concepts of position vector and displacement vector is fundamental. This piece aims to offer a detailed explanation of position vectors and how they differ from displacement vectors.
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A position vector is a mathematical tool used to pinpoint the exact location of an object. It plays a significant role in describing the motion of an object.
A position vector is a vector that denotes the position or location of a specific point with respect to an arbitrary reference point, such as the origin. The direction of the position vector always extends from the origin towards the point in question.
A common practice is to measure the position vector of an object from the origin. Consider a situation where an object is located in space as depicted below:
Position vector
Here,
To find the position vector of any point in the xy-plane, we need to know the coordinates of the point. Let's consider two points A and B with coordinates (x 1 , y 1 ) and (x 2 , y 2 ), respectively. The position vector can be determined by subtracting the corresponding components of A from B:
AB = (x 2 – x 1 ) i + (y 2 – y 1 ) j
The position vector AB starts at point A and ends at point B.
The displacement vector refers to the change in the position vector of an object. Suppose an object is located at point A at time = 0 and moves to point B at time = t. The position vectors of the object at point A and point B are:
Position vector at point
Position vector at point
The displacement vector of the object from time interval 0 to t is:
The displacement of an object can also be defined as the vector distance between the initial and final points. For instance, if an object travels from point A to point B along a black curve:
The displacement of the object is the vector line AB, which runs from point A to point B. The displacement vector always points from the initial point towards the final point.
What is a position vector?
Vectors that specify the position of the body are known as position vectors. Often they start at the origin and terminate at an arbitrary point.
Is velocity a position vector?
Displacement is the vector difference between the ending and starting positions of an object.
What is a displacement vector?
A displacement vector tells you how much the object’s position has changed. The displacement vector includes how far you have travelled and in which direction you have travelled.
What is the formula of position vector?
The position vector of points A and B is AB = (x2 – x1, y2 – y1) = (x2 – x1) i + (y2 – y1) j
What does position vector represent?
A position vector is defined as a vector that indicates either the position or the location of any given point with respect to any arbitrary reference point like the origin.