# Cross Product The cross product of v and w is (almost...) the area of the parallelogram below:    Note this means that the cross product is not commutative (technically it is [anticommutative](https://en.wikipedia.org/wiki/Cross_product#Algebraic_properties)), hence order matters. ### Computation Any time that you see anything related to area in linear algebra the [Determinant](Determinant.md) should immediately pop into mind! Watch [this video](https://youtu.be/eu6i7WJeinw?t=157) for approximately 2 minutes to get a fantastic overview.  ### True cross product Now the true cross product is a not a number-[it is a vector](https://youtu.be/eu6i7WJeinw?t=325)! The cross product will yield a new vector whose magnitude is the area of the parallelogram and whose direction is perpendicular to the parallelogram (where the direction is defined via right hand rule)   --- References: * [Cross product, video 1 - 3b1b](https://www.youtube.com/watch?v=eu6i7WJeinw) * [Cross product, video 2 - 3b1b](https://www.youtube.com/watch?v=BaM7OCEm3G0&t=487s)