Operator: Vector Cross Product

Operator: Vector Cross Product is a Vector Spell Piece added by Psi. It provides the cross product of two vectors, which is defined as $$\vec{v_{1}} \times \vec{v_{2}}=||\vec{v_{1}}||\ ||\vec{v_{2}}||\sin(\theta)$$, where $$\vec{v_{1}}$$ and $$\vec{v_{2}}$$ are vectors, $$||\vec{v_{1}}||$$ and $$||\vec{v_{2}}||$$ are the magnitudes of the two vectors, and $$\theta$$ is the angle between the two vectors. For example, two vectors at a 0° angle to each other (parallel) will have a cross product of 0, while those at a 90° angle will be exactly equal to $$||\vec{v_{1}}|| \times ||\vec{v_{2}}||$$. The result is a vector which is perpendicular to both of the two original vectors. This Operator should not be confused with and. It is unlocked in the lesson "Vectors 101."

A common application of vector cross product is finding the normal vector of a plane (that is, one perfectly perpendicular to said plane) ; Supposing two vectors are not parallel, both can be used at the same time to represent an infinite number of planes parallel to them, and one of the normal vectors to the planes they represent can be obtained as the result of the cross product of those two vectors.

Also, because this vector is perpendicular to both vectors from which it was obtained, it cannot be otherwise obtained from these two vectors as anything but the cross product of the two (i.e it is not a multiple of either, nor the sum or difference between them).

Parameters

 * Vector A: Requires a vector.
 * Vector B: Requires a vector.