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:

- The length of the resulting vector representing the cross-product of two vectors is:

where the vertical bars represent the scalar value of the vector.

- The length of the cross-product of two vectors is equal to the area of the parallelogram determined by the two vectors.

- Multiplication by scalars is commutative. For example, suppose that is a scalar and that is the cross product of respectively , in that case we have that:

- The cross-product is distributive.

- The volume of the parallelepiped determined by the vectors , and is equal to the magnitude of their scalar triple product.

- The vector triple product of the vectors , and is given by:

- Two vectors are parallel if and only if their cross product is the zero 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.

fuss/mathematics/geometry/vectors.txt ยท Last modified: 2017/02/22 18:30 (external edit)

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