Scalar Vs Vector
| Properties | Scalar | Vector |
|---|---|---|
| Definition | A physical quantity that has only magnitude. | A physical quantity that has both magnitude and direction. |
| Direction | Scalar has no direction. (Not applicable) | Vector is Always associated with a specific direction. |
| Representation | Scalar is represented by a number (e.g., 20 kg). | Vector is represented by an arrow showing magnitude and direction. |
| Notation | Scalars are represented by regular letters (e.g., $m$, $t$). | Vectors are represented by bold letters (e.g., F) or with an arrow ($\vec{F}$). |
| Examples | Mass (m), time (t), speed (s), energy (E), temperature (T). | Force ($\vec{F}$), velocity ($\vec{v}$), acceleration ($\vec{a}$), displacement ($\vec{d}$). |
| Mathematical operations | Scalars follow ordinary arithmetic operations (addition, subtraction multiplication, and division). | Vectors follow the rules of vector addition (e.g., triangle/parallelogram law). |
| Change with Direction | Scalars remain the same with the change of direction (Independent of direction). | Vectors do not remain the same with the change of direction. Vectors change when direction changes. |
| Nature | # Scalars are only one-dimensional quantities. # Both scalar and vector can be divided by a scalar. | # Vectors can be Multi-dimensional (i.e. can exist in multiple directions). # A vector can not be divided by a vector. |
| Tensor | Scalar is a tensor of rank-0 | Vector is a tensor of rank-1 |
| Angle | Adding two scalars is independent of the angle. | The resultant vector by adding, subtracting, or multiplying two vectors is dependent on the angle made by those two vectors. |
| Product | The product of two scalars gives only a scalar. | The product of two vectors gives both, scalar (by dot product) and vector by (cross product) |
| Type | Scalar is scalar – no type. | Different types of vectors exist – equal vector, coplanar vector, opposite vector, null vector, unit vector, position vector, parallel vector, etc. |