The position vector which is said to be a straight line having one end fixed to a body and the second end that is attached to a moving point. And this is used to describe the position of the point relative to the body. As the point moves the vector’s position will change in length or in direction or at times in both direction and length. If drawn to some scale, then the change which is in length will signify a change which is in the magnitude of the vector. That is while a change which is in direction will signify a vector that is rotating.
In this article we are going to discover what is a vector as well as a few other important points.
The velocity and the position vectors which are of a particle are illustrated in Figure given below. The position vector which is denoted by r extends from the origin to the particle. While the velocity vector which is denoted by letter v points in the direction of the particle’s motion. The other variables which are appropriate one are for describing a moving particle that can be defined in terms of these variables and the elementary variables as well.
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The momentum which is denoted by letter p of the particle is equal to the product of the velocity and mass that is v of the particle
We shall find the momentum which is useful for describing the motion that is of electrons in a system which is extended such as a crystal.
The particle's motion which is moving about a center of force can be described using the angular momentum. That is defined to be the cross product of the position and vectors momentum which is given as:
The cross product that is of two vectors is a vector which is having a magnitude equal to the product of the magnitudes of the two vectors and at times the same as the sine of the angle between them. This is denoting the angle which is between the momentum and position vectors by θ as the magnitude of the momentum that is the angular vector momentum can be written as:
We can use a vector which is known as the position vector to tell us the location of one object that is relative to another. Specifically we can say that a position vector is:
A vector that indicates the position of a given point with respect to an arbitrary reference point example origin.
In this article we will discuss the following aspects of position vectors:
Explain what is a Position Vector?
And how to Find the Position Vector?
Often, we have noticed that the vectors start at the origin and terminate at any arbitrary point are known as position vectors. These are said to determine the position of a point with reference to the origin of that point.
The direction of the vectors or the position vector generally points from the origin towards the given point. In the coordinate system of c\Cartesian if point O is the origin and Q is some point that is x1, y1, then the directed position vector from point O to point Q is represented as OQ. In the space which is three-dimensional if O = (0,0,0) and Q = (x1, y1, z1), then the position vector denoted by r of point Q is represented is:
r = x1i + y1j + z1k
Now let’s suppose that we have two vectors, that are A and B, with position vectors we write a = (2,4) and b = (3, 5) respectively. We can then write the coordinates of both the vectors that are A and B as:
A = (2,4), B = (3, 5)
Here before determining the position vector of a point we first need to determine the coordinates of those particular pointst. Let’s suppose that we have two points, namely M and N. where the point M = (x1, y1) and N = (x2, y2). Next we want to find here the position vector that too from point M to point N the vector MN. To determine this position vector, we simply subtract the corresponding components of M from N:
Written as : MN = (x2-x1, y2-y1)
If we consider a point denoted by letter P. Which has the coordinates that are xk, yk in the xy-plane and another point written as Q. Which has the coordinates denoted by xk+1, yk+1. The formula which is to determine the position vector that is from P to Q is written as:
PQ = ((xk+1)-xk, (yk+1)-yk)
We can now remember the position vector that is PQ which generally refers to a vector that starts at the point P and ends at the point Q. Similarly if we want to find the position vector that is from the point Q to the point P then we can write:
QP = (xk – (xk+1), yk – (yk+1))
Q1. Explain What is Meant By Position Vector?
Ans: We can say that the position vector which is a straight line that is having one end fixed to a body and the other end attached to a moving point and it is used to describe the position of the point which is a relative point to the body. As the point usually moves, the position vector will also change in length or we can say in direction or in both length and direction.
Q2. Explain is a Position a Vector?
Ans: The position of an object is generally given relative to some agreed upon reference point. We can say that the position is a vector quantity. It has a magnitude along with a direction. The magnitude which is a quantity of vectors is a number with units that is telling us how much of the quantity there is and the direction tells us which way it is pointing.
Q3. Explain What is the Position and Displacement Vector?
Ans: The vector which is the position vector is used to specify the position of a certain body. The term displacement vector is used to find the change that is in the position vector of an object. The vector which generally represents the position of an object and the origin as the frame of reference is known as position vector.
Q4. Explain Can a Position Vector be Negative?
Ans: If there are two vectors that are having the same magnitude that is size and the same direction also. Then we can generally call them equal to each other. Just like the scalars which can have negative or the positive values. The vectors can also be negative or positive. A vector which is the negative is a vector which points in the direction opposite to the reference positive direction.