 asked in category: General Last Updated: 9th April, 2020

# Is AxB a BxA?

The cross product is a vector perpendicular to both the crossed vectors and its length is the area of the parallelogram you get, the deal is that either up or down works for this definition so we just have to define either 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).

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9th April, 2020

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