##### Asked by: Bertha Weinheimer

asked in category: General Last Updated: 9th April, 2020# Is AxB a BxA?

**AxB**or

**BxA**as up and then the other down, which is why

**AxB**=-

**BxA**.

Just so, what is AxB?

Definition: For sets A and B, the Cartesian prod- uct of A and B, denoted **AxB**, is the set of all ordered pairs (a, b) such that a ∈ A and b ∈ B. That is, **AxB** = {(a, b)|a ∈ A ∧ b ∈ B}. Example: A = {0,1}, B = {a, b, c}. **What** is **AxB**?

Similarly, why AxB is not equal to BxA? Cartesian product sets. Generally speaking, **AxB** does **not equal BxA** unless A=B or A or B is the empty set. This is usually easy to explain to students because in the definition of a cartesian product, we define it as an ordered pair, meaning order would matter.

In this regard, how is AxB calculated?

Magnitude: |**AxB**| = A B sinθ. Just like the dot product, θ is the angle between the vectors A and B when they are drawn tail-to-tail. Direction: The vector **AxB** is perpendicular to the plane formed by A and B. Use the right-hand-rule (RHR) to find out whether it is pointing into or out of the plane.

Is AxB XC ax Bxc?

That is, **a x** (**b x c**) lies in the plane of b and c. Consequently, (**a x b**) **x c**, which is the same as −c x (**a x b**), will lie in the plane of a and b. Hence, (**a x b**) **x c** will, in general, be different from **a x** (**b x c**).