The result of the cross-product of a two vectors is another vector. Given two vectors and , their cross-product can be written as:
or, using determinants:
which is derived from:
where the vertical bars represent the scalar value of the vector.
One solution to find the area of a triangle is to determine its height and then proceed to the multiply the height by the base and divide by two. However, that may be a difficult task and instead, by using the parallelogram property of vectors, one can calculate the area of the parallelogram and then divide the area by two.