Why do we multiply two vectors to get a third?
In short: Most students memorize the cross product formula without understanding its purpose. This video reverses that process, starting with the geometric goals of the operation before deriving the algebra.
The cross product is a specific method for multiplying two three-dimensional vectors to produce a third vector. Rather than leading with complex calculations, Dr. Trefor Bazett explores why this operation exists in mathematics by focusing on two primary geometric objectives: finding orthogonal vectors and calculating the area of a parallelogram.
By understanding these goals first, the algebraic computation becomes a logical consequence of geometry rather than an arbitrary rule to memorize.
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Sources
- Summary by Intellect · source: Geometrically Defining the Cross Product | Multivariable Calculus
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