Math Hacks: Vectors - Cross Product

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Издатель Dec 5, 2022

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Hi there! In this video, we are covering one of the two ways to multiplying vectors together! We can multiply two vectors together to produce a scalar result through dot product, or a vector result through cross product--and both have many useful applications! In this video, we are focusing on how to calculate cross product!

The cross product of two vectors can be calculated using the formulas:

a x b = |a||b|sinθ(n) or a x b = ([aybz - azby], [azbx - axbz], [axby - aybx])

Both formulas have many applications, but often the second one is easier to use to calculate the cross product as we don't need to solve for the unit vector n! While it may be difficult to memorize, there are a variety of memory techniques I will highlight in future videos!

Important to note, the cross product will be a maximum when the two vectors are perpendicular to each other, and will be a minimum (equal to zero) when they are parallel (or with a 180 degree angle between them)!

For additional videos on vectors, check out my playlist below:
https://www.youtube.com/playlist?list=PLmf_492Ha0RGecxMWBciguFPTj-fm_BKr

For a videos instead covering dot product, check out these shorts below:
https://youtube.com/shorts/OfXsglFmoew?feature=share
https://youtube.com/shorts/OtUPvX1-bMg?feature=share
https://youtube.com/shorts/70tUjidptNc?feature=share