Question

What is the physical meaning of cross-product?

Answer 1

Hint: For a resultant vector, the cross product is known as the vector product of the two vectors and can be written as A x B. This resultant vector illustrates a cross-product between two vectors on a plane surface.

Complete step by step solution:
We know that A vector is a quantity with magnitude and direction used to locate one location in space in relation to another. It can be visualized as an arrow or a line segment with the direction in a geometrical representation.

Mathematically, the cross product of two non-zero vectors \[\overrightarrow a \] and \[\overrightarrow b \] , is
\[\overrightarrow a \times \overrightarrow b = |\overrightarrow a ||\overrightarrow b |sin\,\theta \widehat {\,n}\]
Where \[\theta \] is the angle between \[\overrightarrow a \] and \[\overrightarrow b \] , \[0 \leqslant \theta \leqslant \pi \] . Also, \[\widehat n\] is a unit vector perpendicular to both \[\overrightarrow a \] and \[\overrightarrow b \] such that \[\overrightarrow a ,\overrightarrow b \] and \[\widehat {\,n}\] form a right-handed system.

Image: cross product of two vectors

Hence, the physical meaning of cross product is a vector that is perpendicular to the two vectors is the cross product of any two vectors. It has magnitude as well as direction. The resultant vector has the same magnitude as the parallelogram, whose side lengths are the same as the magnitudes of the two provided vectors.

Note: Students should remember the right-hand thumb rule in which you stretch your right hand so that the index finger of the right hand is in the direction of the first vector and the middle finger is in the direction of the second vector. Then, the thumb of the right hand indicates the direction vector.