Question

Why cross product is a vector quantity ?

Answer 1

Dot product

1. A dot product or scalar product is the product of two vectors.
2. The resultant of the dot product is a scalar.
3. If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two two, their dot product is given by $\overrightarrow{A}·\overrightarrow{B}$. It has only magnitude.
4. $\overrightarrow{A}·\overrightarrow{B}=\left|A\right|\left|B\right|\cos \theta$.

Cross product

1. A Cross product or vector product is the product of two vectors.
2. The resultant of the cross product is a vector perpendicular to the plane of the two vectors.
3. Since the resultant is a vector hence it has both magnitude and direction.
4. Therefore the cross product is a vector.
5. If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors, their cross product is given by $\overrightarrow{A}\times \overrightarrow{B}$. It has both magnitude and direction.
6. $\overrightarrow{A}\times \overrightarrow{B}=\left|\overrightarrow{A}\right|\left|\overrightarrow{B}\right|\sin \theta$.

From the above information, it is clear that cross-product is always a vector quantity.