Scalar vs Vector – Difference and Comparison

What is Scalar?

Scalars are physical quantities their magnitude can fully represent; examples include mass, speed, and volume. Furthermore, depending on how it is applied, the product of two vector values might either be a vector or a scalar. Scalar’s magnitude serves as its sole description.

A few scalars are volume, density, speed, energy, mass, and time. Other quantities, like force and velocity, are referred to as vectors because they have both magnitude and direction. The standard algebraic principles can be used to modify scalars.

Real numbers are positive but do not always characterize scalars. When a particle moves in the opposite direction from the direction in which a force is acting, as when frictional force slows down a moving body, for instance, the work done on the particle by force is a negative quantity.

Scalar quantities are one-dimensional parameters that lack direction and merely have magnitude. They are, therefore, just numbers with matching units. Scalars, including length, mass, duration, and speed, lack direction because their values do not change; they can be applied in any direction.

Scalar values can be combined according to the same algebraic rules as integers, allowing them to be added, subtracted, or multiplied. This makes it possible to compare two or more scalar quantities quantitatively.

What is Vector?

A vector quantity is a physical quantity that has both magnitude and direction. A vector quantity is represented by a vector, which is an arrow that indicates both the magnitude and direction of the quantity.

Vector quantities are often written in boldface to distinguish them from scalar quantities, which have only magnitude. According to the definition of a vector quantity, a vector can only be solved using vector algebra. An arrow put over the vector’s magnitude indicates a vector quantity. For instance, vector quantities include velocity, force, and displacement.

The standard unit for length is the meter, symbolized by m. Other examples of vector quantities include electric field, magnetic field, and momentum. A vector quantity has a specified direction as well as a magnitude associated with the unit. As a result, when creating or declaring a vector quantity, the direction of activity and its value or magnitude must be described.

The magnitude of a vector specifies the size of the quantity, which is also its absolute value, and the direction denotes the side, such as east, west, north, or south. Vector quantities are expressed in one-dimensional, two-dimensional, or three-dimensional parameters.

Any change in the vector quantity indicates a change in the magnitude, direction, or both. A vector can be resolved using the sine or cosine of neighboring angles (vector resolution).

Difference Between Scalar and Vector

There is a distinction between a scalar and a vector in physics. Vector quantities are often written in boldface to distinguish them from scalar quantities, which have only magnitude.

A scalar is a physical quantity with no direction and simply magnitude. A vector is a physical quantity with a magnitude as well as direction.

A vector is a collection of ordered numerical values, whereas a scalar is a single numerical value. A vector is represented as a line segment with magnitude and direction. The magnitude of the line defines its length.

Comparison Between Scalar and Vector

Parameter of ComparisonScalarVector  
Simply means  Without direction and merely has magnitude.  Contains magnitude and direction.
DimensionsOnly one dimension  Multiple dimensions
Alter  It alters as their magnitude fluctuates.  When their magnitude, direction, or both changes, it also changes.
ResponseBecause a scalar amount always has the same value regardless of direction, it cannot be resolved.Angle can be used to resolve any vector quantity.
ExampleA Vehicle is travelling at 60 kilometers per hour.A vehicle is travelling eastward at a speed of 30 kilometers per hour.

References

  1. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.98.104035
  2. https://ieeexplore.ieee.org/abstract/document/582476