The cross product of two vectors  and  is defined only in three-dimensional space and is denoted by .

Reasoning :

(1).

In two dimensional space, the system consists of a pair of lines on a flat surface or plane, that

intersect at right angles. The lines are called axis  and the point at which they intersect is called as origin.

(2)

The axes are usually drawn horizontally and vertically and are referred to as the -axis and

-axes, respectively.

(3).

The cross product is fundamentally a directed area and the direction of the cross product is given

by the right-hand rule.

The cross product is not cummutative.

Therefore the cross product is not defined in two dimensional coordinate system.

Cross product is not defined in two dimensional coordinate system.