Answer:
See explanation below.
Step-by-step explanation:
Definition
The cross product is a binary operation between two vectors defined as following:
Let two vectors 
The cross product is defined as:

The last one is the math definition but we have a geometric interpretation as well.
We define the angle between two vectors a and b
and we assume that
and we have the following equation:

And then we conclude that the cross product is orthogonal to both of the original vectors.
Some properties
Let a and b vectors
If two vectors a and b are parallel that implies 
If
then
is orthogonal to both a and b.
Let u,v,w vectors and c a scalar we have:

(Distributive property)

Other application of the cross product are related to find the area of a parallelogram for two dimensions where:

And when we want to find the volume of a parallelepiped in 3 dimensions:
