Vector Product or Cross Product of Two Vectors
If we get a vector quantity on multiplying two vector quantities, then this product is called a vector product or a cross product. Vector product is expressed by putting a cross (X) mark between the two vectors.
The vector product of two vectors \(\vec A\) and \(\vec B\) is another vector \(\vec C\), whose magnitude is equal to the product of the magnitudes of the two vectors and sine of the angle between them.
Let the magnitudes of the vectors \(\vec A\) and \(\vec B\) be A and B, and the angle between them be θ. Then, the vector product is given as:
\(\vec { A } \times \vec { B } =\left| \vec { A } \right| \vec { B } |\sin \theta \hat { n } \)
or \(\vec { A } \times \vec { B } =AB\sin \theta \hat { n }\) …………….. (i)
Here, \(\hat n\) is the unit vector in the direction of the magnitude of the resultant vector. its direction is perpendicular to the plane of vector \(\vec A\) and \(\vec B\).
