Following are the differences between scalar product and vector product of two vectors:
| Scalar Product | Vector Product |
| When two vectors are multiplied in such a way that their product is a scalar quantity then it is called scalar product. | When two vectors are multiplied in such a way that their product is a vector quantity then it is called vector product. |
| Scalar product of two vectors $\vec{A}$ and $\vec{B}$, denoted by $\vec{A}.\vec{B}$ is $\vec{A}.\vec{B}=AB\cos\theta.$ | Vector product of two vectors $\vec{A}$ and $\vec{B}$, denoted by $\vec{A}×\vec{B}$ is $\vec{A}×\vec{B}=AB\sin\theta\:\hat{n}$ where $\hat{n}$ is a unit vector in the direction of $\vec{A}×\vec{B}.$ |
| It is also called dot product. | It is also called cross product. |
| It acts along the same plane as the two vectors. | It acts normally to the plane formed by the two vectors. |
| It follows commutative law i.e. \[\vec{A}.\vec{B}=\vec{B}.\vec{A}\] | It does not follow commutative law i.e. \[\vec{A}×\vec{B}≠\vec{B}×\vec{A}\] |
| Scalar product of two equal vectors is square of the magnitude of either vector i.e. \[\vec{A}.\vec{A}=A^2\] | Vector product of two equal vectors is zero i.e. \[\vec{A}×\vec{B}=0\] |
| Scalar product of two perpendicular vectors is zero. | Magnitude of vector product of two perpendicular vectors is equal to the product of magnitude of each vector. |
| It is the product of magnitude of projection of either vector on another vector and magnitude of the another vector. | Its magnitude represents the area of the parallelogram bounded by the two vectors. |