Difference Between Scalar and Vector
Main difference
The main difference between Scalar and Vector is that Scalar is known as the quantity that comprises the only magnitude and has no direction whereas Vector is known as the physical quantity, which consists of the direction and the magnitude.
Scalar vs Vector
The scalar contains only the magnitude and has no direction; on the other hand, Vector contains both the magnitude and the direction. The Vector consists of the only dimension and is considered one-dimensional; on the contrary, Vector contains many dimensions, so it is considered multidimensional.
The scalar quantity changes when the change in its magnitude occurs; on the other hand, the vector quantity alternates when the variation occurs in its magnitude or direction. The standard rules of algebra apply in the case of scalar; At the same time, different sets of vector algebraic rules are followed and are known as vector algebra.
The scalar quantity can be divided with another scalar quantity; on the other hand, a vector quantity cannot be divided by 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 using a unit limit, or using the arrow at the top. The symbol for a scalar is a symbol for quantity; however, by contrast, the symbol for a vector is a quantity symbol and an arrow sign at the top.
Some examples of a scalar quantity are energy, mass, length, temperature, and density, while some instances of the vector are acceleration, weight, displacement, force, and velocity.
Comparison chart
| Climb | Vector |
| The physical quantity that does not contain any direction and consists of only magnitude is known as scalar. | The implication of a physical quantity consisting of both direction and magnitude is known as a vector. |
| Sense | |
| It contains only the magnitude and has no direction. | It also contains the magnitude and direction. |
| dimensional quantities | |
| It consists of the only dimension and is considered one-dimensional. | It contains many dimensions, so it is considered multidimensional. |
| Change in quantity means | |
| It changes when the change in its magnitude occurs. | It alternates when the variation arrives in its magnitude or direction. |
| algebra rules | |
| In this case common rules of algebra apply. | In this case, a different set of algebraic rules is followed and is known as vector algebra. |
| Division | |
| The scalar quantity can be divided into another scalar quantity. | A vector quantity cannot be divided into another vector quantity. |
| Comparison of two quantities | |
| The comparison between two scalar quantities is relatively simple. | The contrast between the two vector quantities is comparatively complex. |
| Represented by | |
| It can be represented by a unit and a magnitude (number). | It can be represented by a unit and magnitude (number), direction using a unit limit, or using the arrow at the top. |
| symbols | |
| The symbol for a scalar is a symbol for quantity. | The symbol for a vector is a quantity symbol and an arrow sign at the top. |
| Solve in directions | |
| It cannot resolve to any address because it consists of the same value regardless of an address. | It can be solved in any direction using the sine or cosine of adjacent angles. |
| Math operation | |
| The mathematical operation that occurs between two scalar quantities will always result in a scalar; however, if a scalar quantity is operated on with any vector quantity, the result will be a vector. | The mathematical operation between two or many vectors can give a vector or a scalar quantity, as dot multiplication of two vectors gives Scalar. In contrast, cross multiplication, subtraction, or addition between two vectors will always result in a vector. |
| examples | |
| Some examples of a scalar quantity are energy, mass, length, temperature, and density. | Some examples of Vector are acceleration, weight, displacement, force, and velocity. |
What is Scaling?
A type of physical quantity in which the dimension is defined only by the magnitude of the quantity, not the direction, is then called a scalar. The scalar quantity never consists of a direction because it only deals with the magnitude of an object.
In the scenario of a scalar, when some change in quantity is noticed, it is only because a change in its magnitude occurs. Normally, scalar quantities follow the common laws of algebraic rules, and that is why they can be easily subtracted, added, divided, or multiplied algebraically, just like standard numbers, although scalar quantities must contain the exact units.
What is Vector?
The quantity by which dimension is taken by both the direction and magnitude of an object is commonly known as a vector. When two quantities have the same magnitude and a similar direction, these two quantities will be called vector quantities.
When an alternation occurs in both magnitude and direction, this will result in the change in a vector quantity. The vector quantity generally does not follow the basic rules of algebra because the direction is linked with the vector quantity, but instead follows the algebraic vector laws. Some examples of Vector are acceleration, weight, displacement, force, and velocity.
Key differences
- Quantity that consists only of magnitude, but does not have a direction, is known as a scalar; On the other hand, the quantity that includes both the direction of a quantity and a magnitude is also known as a vector.
- Each scalar quantity is considered one-dimensional because it consists of only one dimension; on the contrary, the vector quantity is considered multidimensional because it consists of one, two or three dimensions.
- When any change in the magnitude of a scalar quantity occurs, the scalar quantity will also change; on the other hand, any change in the direction or magnitude of a vector quantity will also change the vector.
- A scalar number cannot be resolved into any direction because it always has the same value despite having an address; conversely, the vector quantity can be determined in any kind of direction using the sine or cosine of any adjacent angle.
- When a mathematical expression is drawn 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 other hand, when a mathematical operation is performed between two vectors, then the result will always be a vector or perhaps a scalar, for example dot multiplication between two vectors usually results in a scalar. In contrast, addition, subtraction, or cross multiplication gives only one vector.
- Some 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.
Final Thought
The above discussion concludes that if a quantity consists of only one magnitude, then it will be known as a scalar quantity; conversely, if a quantity consists of both direction and magnitude, then it will be a vector quantity.