Vector and Scalar Quantities

William Rowan Hamilton, an Irish physicist, is credited with developing vectors. Josiah Willard Gibbs and Oliver Heaviside invented vectors in their modern form. They used it to express James Clerk Maxwell’s laws of electromagnetic.

Physical quantities can be classified in two ways in mathematics and physics, namely Scalar Quantity and Vector Quantity. If we pay attention, we’ll observe that our environment has two types of quantities and processes. One is dependent on the direction in which they occur, while the other is unaffected by direction.

If the amount varies on the direction, mathematicians and scientists call it a ’vector.’ If the number does not rely on direction, it is referred to as ‘scalar.’

Definition of scalar quantities :-

Scalar quantities are the physical quantities that have only one magnitude. It can be adequately described by a numerical value or a magnitude. There are no directions for a scalar quantity. In other words, a scalar is a quantitative measurement. 

Scalar quantities are physical quantities that can be fully expressed by a single number and an appropriate unit. Number is a synonym for scalar.

For example, if Ramu says that the tower’s height is 15 cm , then the tower’s height is a scalar quantity because it just requires the magnitude of height to define itself.

Some examples of scalar quantities :-

In mass, there is no direction, only value. As a result, it’s a scalar quantity. Scalar quantities include time, distance, temperature, length, volume, and energy. The electric charge has no direction and just has a value. As a result, this is likewise a scalar quantity. Scalar quantities include speed and power, to name a few. Mass, speed, distance, time, energy, density, volume, temperature, distance, work, etc are the examples of the scalar quantities.

Definition of vector quantities :-

Vector quantities are physical quantities for which both magnitude as well as the direction are clearly defined.

For example, if we wish to travel to a location we have never been before, we need to know not only the distance but also the direction of our destination. As a result, vector quantities are characterised in terms of both magnitude and direction. Knowing about vectors is essential if you’re researching motion. Complex multi-dimensional problems can be viewed as one-dimensional problems using vectors.

Some examples of vector quantities :-

 force has a value and a direction, a simple example of a vector quantity is a pull or a push. We apply force (magnitude) when we pull or push something, but it always includes a direction. Weight has both a value and a direction. Your mass (magnitude) is directly proportional to your weight, which is always in the direction of the earth’s centre. Velocity, acceleration, displacement, and momentum are all instances of vector quantities.

Addition of vectors :-

The diagonal of a parallelogram or the law of parallelogram can be described as the addition of two vectors. When two vectors, A and B, are placed at the same point and are represented in magnitude and direction by the diagonal of the parallelogram that passes through the same point, the result is in magnitude and direction by the diagonal of the parallelogram that passes through the same point, according to this law.

Subtraction of

Some basic facts about scalar and vector quantities :-

• Many branches of mathematics and science rely heavily on vectors and scalars.
• In two-dimensional or three-dimensional space, vectors can be expressed. In computers, vector graphics are sometimes employed. Vectors can be scaled up to several times their original size without sacrificing image quality.
• When two vectors are cross-products, a new vector is created whose direction is orthogonal to both of the original vectors. The right-hand thumb rule, which you’ve probably studied in Physics, is a good example of this.

CONCLUSION :-

Many topics in physics are built on the foundation of vector and scalar quantities. As a result, you can see how critical it is not only for mathematics but also for other courses. Vectors have both a magnitude and a direction.It defies the standard rules of algebra. Either the magnitude or the direction of change changes, or both. Scalar quantities are the physical quantities that have only one magnitude. It can be adequately described by a numerical value or a magnitude