Difference between Scalar and Vector Products of Two Vectors

Following are the differences between scalar product and vector product of two vectors:

Scalar ProductVector 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.

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