.. Explain scalar and vector quantities. Explain the laws involved in addition and
subtraction of vectors.
Answers
Answer:
Mathematics and Science were invented by humans to understand and describe the world around us. A lot of mathematical quantities are used in Physics to explain the concepts clearly. A few examples of these include force, speed, velocity and work. These quantities are often described as being a scalar or a vector quantity. Scalars and vectors are differentiated depending on their definition. A scalar quantity is defined as the physical quantity that has only magnitude, for example, mass and electric charge. On the other hand, a vector quantity is defined as the physical quantity that has both magnitude as well as direction like force and weight. The other way of differentiating these two quantities is by using a notation. In this article, let us try to learn what is a vector and a scalar quantity.
Scalar quantity is defined as the physical quantity with magnitude and no direction.
Some physical quantities can be described just by their numerical value (with their respective units) without directions (they don’t have any direction). The addition of these physical quantities follows the simple rules of the algebra. Here, only their magnitudes are added.
Examples of Scalar Quantities
There are plenty of scalar quantity examples, some of the common examples are:
Mass
Speed
Distance
Time
Area
Volume
Density
Temperature
What is a Vector Quantity?
A vector quantity is defined as the physical quantity that has both direction as well as magnitude.
A vector with the value of magnitude equal to one and direction is called unit vector represented by a lowercase alphabet with a “hat” circumflex. That is “û“.
Examples of Vector Quantities
Vector quantity examples are many, some of them are given below:
Linear momentum
Acceleration
Displacement
Momentum
Angular velocity
Force
Electric field
Polarization
After understanding what is a vector, let’s learn vector addition and subtraction. The addition and subtraction of vector quantities does not follow the simple arithmetic rules. A special set of rules are followed for the addition and subtraction of vectors. Following are some points to be noted while adding vectors:
Addition of vectors means finding the resultant of a number of vectors acting on a body.
The component vectors whose resultant is to be calculated are independent of each other. Each vector acts as if the other vectors were absent.
Vectors can be added geometrically but not algebraically.
Vector addition is commutative in nature, i.e., →A+→B=→B+→A
Now, talking about vector subtraction, it is the same as adding the negative of the vector to be subtracted. TO better understand, let us look at the example given below.
Let us consider two vectors →A and →B as shown in the figure below. We required to subtract →B from →A. It is just the same as adding →−B and →A. The resultant is shown in the figure below
Subtraction of Vectors
Explanation:
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