The cross product is a geometric operation that takes 2 vectors in 3 dimensional Euclidean space and returns a vector that is perpendicular to the plane between both input vectors.
The cross product is only defined in 3 dimensional Euclidean space and is usually represented using a
The cross product can be calculated geometrically as follows:
Where
The cross product can be defined with the notation of determinants as follows:
To calculate the area of the parallelogram formed between
Find the cross product
Find the cross product
Find two unit vectors orthogonal to
Find a unit vector with positive first coordinate that is orthogonal to the plane through the points