Is the Vector Product Really a Vector?

[golshah]

Homework Statement

How can I prove that the vector (cross or external) product is really and physically a vector. I face with this problem in math physics course.
thanks for your hint.

Homework Equations

The Attempt at a Solution

 

[willem2]

I think the fact that the crossproduct is a vector follows immediately from the definition of the cross product.

 

[Liquidxlax]

you find torque with the cross product you need two vectors in order to find it and the resulting torque is normal to the other 2

 

[fzero]

What are you using as a definition of a vector? For example, does a vector obey a certain transformation rule? Does the cross product satisfy the required properties.