The key difference between scalars and vectors can be explained as that scalar quantities need the only magnitude for their elaboration while vector quantities need both magnitude and direction for their elaboration.
Both scalar and vector quantities represent physical quantities, and both are measurable. Both define the certain magnitude of quantities, but vector quantities also specify the direction of the quantity. It can be said that a scalar is a quantity that is measured in one dimension, i.e. magnitude while vector is the quantities which are multidimensional, needing both magnitude and direction of the physical quantity.
If we want to change a scalar quantity, the only change requires will be in their magnitude while if we want to change a vector quantity, we can change either its magnitude or direction or both.
Vector quantities are just numerical figures, so they follow the usual rules of the algebra. They can be added, subtracted, multiplied or divided while vector quantities do not follow the rules of ordinary algebra. They are calculated by certain specific rules called the rules of vector algebra.
Two scalars can divide each other while two vectors cannot divide each other. The product of two scalar quantities is always a scalar quantity while the product of two vector quantities may be a scalar or a vector quantity. Any mathematical procedure between a scalar and vector quantity will result in a vector quantity.
Both scalar and vector quantities need units for their expression. Scalar quantities are denoted by simple alphabets like v for speed while vector quantities are denoted by boldface letters like V for velocity. They can also be dented by putting an arrowhead on the alphabet.
Unit vectors are also used in physics. They have a magnitude of 1. They are used only to express the direction. While no such type of unit scalar is used in physics. Vectors graphics are also in use nowadays in computers because they can be drawn to a large size with good graphics quality. It is impossible for a scalar quantity to be resolved in parts. It has uniform value in all the directions. While vector quantities can be resolved in two perpendicular directions using the angle between them. If we say that a car is moving at a speed of 30 Km per hour it will indicate the speed of the car which is a scalar quantity and if we say that a car is moving with a speed of 30 Km per hour in the East it will indicate the velocity of the car which is vector quantity.
Comparison chart
| Basis | Scalar Quantity | Vector Quantity |
| Definition | A scalar is a quantity which needs only its magnitude for complete expression. | A vector is a quantity which needs both magnitude and direction for complete expression. |
| Change | A change in it will require only the change in its magnitude. | A change in it will require either the change in its magnitude or direction or both. |
| Mathematical procedures | They can be multiplied, subtracted or added using the common rules of the algebra. | They cannot be operated by using the simple rules of the algebra. Vector algebra rules are used to operate them. |
| Expression | They are denoted by simple alphabets, e.g. V for velocity. | They are denoted by boldface letters, e.g. V for velocity or putting an arrowhead over the letter. |
| Division | Two scalars can divide each other. | Two vectors cannot divide each other. |
| Product | The product of two scalar quantities is always a scalar. | The product of two vector quantities may be a scalar or a vector. |
| Resolution | It is not possible for a scalar to be resolved in parts. | It is quite possible for a vector to be resolved in parts. |
| Unit scalar or unit vector | Unit scalars are not used in physics. | Unit vectors are used in physics to indicate direction. |
| Product with each other | Their product with a vector will result in a vector. | Their product with a scalar will result in a vector. |
| Example | A car is moving at a speed of 30 Km per hour. | A car is moving with a velocity of 30 Km per hour in the East. |
What is a Scalar Quantity?
A scalar is a quantity which is uni-dimensional, i.e. its whole understanding need only its magnitude and measuring unit. No need of direction to elaborate it. For example the temperature of an object, the mass of a body and speed of a car etc. The rules of general algebra are applied to the scalar quantities because they are just the figures. They are denoted by simple alphabets, e.g. M for mass, T for temperature and V for speed. A change in the magnitude of the scalar quantity will change the quantity as a whole while any change in the direction will have no effect on the quantity.
Examples of Scalar Quantities
- Heat
- Density
- Length
- Calorie
- Charge
- Speed
- Mass
- Frequency
- Kinetic energy
What is a Vector Quantity?
Vectors are those quantities which have more than one dimension for their complete elaboration. They not only need magnitude but also direction for the understanding of their meaning. Vectors do not follow the usual rules of algebra rather they follow the triangle law of addition. They are liable to be resolved into individual parts, unlike the scalars. They are denoted by boldface letters, e.g. V for velocity and a for acceleration. They can also be expressed by putting arrowhead above them.
Examples of Vector Quantities
- Force
- Acceleration
- Velocity
- Momentum
- Torque
- Centrifugal force
- Electric field intensity
Key Differences between Scalar Quantity and Vector Quantity
- Scalar quantities need the only magnitude for their complete understanding while vectors need both magnitude and direction.
- Scalar quantities can be operated by simple rules of algebra while vector quantities cannot be operated by them.
- Scalar quantities are represented by simple letters while vector quantities are represented by boldface letters.
- If two scalar quantities are multiplied, their product is always a scalar while the product of two vectors may be a scalar or a vector.
- Unit vectors are used in physics to indicate direction while unit scalars are not used.
Conclusion
Scalar and vector quantities are the base of physics. We also encountered various vectors and scalars in our daily life. It is compulsive to know the difference between them. In the above article, we learned about clear differences between scalars and vectors.
quite good explanation, i’m fully satisfied with this explanation