The main difference between Scalar and Vector is that Scalar is known as the quantity which comprises the only magnitude and does not have any direction, whereas Vector is known as the physical quantity, which consists of both direction and the magnitude.
Scalar vs. Vector
The Scalar contains only the magnitude and does not have any direction; on the other hand, Vector contains both the magnitude and direction as well. The Vector consists of the only dimension and considered as one dimensional; on the contrary, Vector contains many dimensions, so it is regarded as multidimensional.
The scalar quantity changes when the change occurs in its magnitude; on the flip side, the vector quantity alternates when the variation comes in its magnitude or direction. Standard rules of algebra are applicable in the case of scalar; at the same time, different sets of algebraic rules are followed in vector and known as vector algebra.
The one scalar quantity can be divided with other scalar quantity; on the other hand, one vector quantity could not be divided with another vector quantity. The comparison between two scalar numbers is relatively simple; on the contrary, the correlation between two vector quantities is comparatively complicated.
The scalar can be represented by a unit and a magnitude (number); on the other hand, a vector quantity can be represented by a unit, and magnitude (number), direction by using a unit cap, or by using the arrow at the top. The symbol of a scalar is a quantity symbol; however, on the contrary, the symbol of a vector is a quantity symbol and a sign of arrow at the top.
Some examples of a scalar quantity are energy, mass, length, temperature, and density, while some cases of the vector are acceleration, weight, displacement, force, and velocity.
What is Scalar?
A kind of physical quantity in which the dimension is defined only by the magnitude of the quantity, not direction, then it is called a scalar. The scalar quantity never consists of a direction because it takes concern only with the magnitude of an object.
In the scenario of a scalar, when any change is noticed in quantity, then it is only because of a change occurs in its magnitude. Typically, the scalar quantities follow the common laws of algebraic rules, and that is why they can easily be subtracted, added, divided, or multiplied algebraically, just like standard numbers though scalar quantities must contain the exact units.
What is Vector?
The quantity in which the dimension is taken by both the direction and magnitude of an object is commonly known as a vector. When two quantity consists of the same magnitude and a similar direction, then these two quantities will be called as vector quantities.
When an alternation occurs in both the magnitude and direction, then this will result in the change in a vector quantity. The vector quantity usually does not follow the basic rules of algebra because the direction is linked with the vector quantity, instead follows algebraic vector laws. Some examples of Vector are acceleration, weight, displacement, force, and velocity.
- The amount which consists of only the magnitude, but does not have a direction is known as scalar; on the flip side, the quantity which includes both the direction of a quantity and a magnitude as well is known as vector.
- Every scalar quantity is considered one dimensional because it consists of only one dimension; on the contrary, the vector quantity is considered as multidimensional because it consists of one, two, or three dimensions.
- When any change occurs in the magnitude of a scalar quantity, the scalar quantity will also be changed; on the other hand, any change occurs in direction or the magnitude of a vector quantity, the vector will also be modified as well.
- A scalar number cannot be resolved in any direction because it always consists of the same value despite having direction; in contrast, the vector quantity can be determined in any type of direction by using the sine or cosine of any adjacent angle.
- When a mathematical expression is taken out between two scalar numbers, the answer will be a scalar; however, when the mathematical expression is taken between a scalar and a vector quantity, the result will always be a vector. On the flip side, when a mathematical operation is done between two vectors, then the result will always be a vector or maybe a scalar, for instance, the dot multiplication between two vectors usually results in a scalar. In contrast, the summation, subtraction, or a cross-multiplication gives only a vector.
- A few examples of a scalar quantity are energy, mass, length, temperature, and density, while some examples of the vector are acceleration, weight, displacement, force, and velocity.
The above discussion concludes that if a quantity consists of only a magnitude, then it will be known as a scalar quantity; in contrast, if a quantity consists of both the direction and magnitude, then it will be a vector quantity.