76 - The Cross Product

The cross product is written as and gives a vector with two special properties.
It is given by , but a better way to find it is by the determinant of the 3x3 matrix formed by the unit vector on the first row and each vector on the second and third row.

The cross product of two vectors is perpendicular to both of them

This means that the dot product of a vector and its cross product is zero. The cross product only works in three dimensions

The length of the cross product is a measure of how far apart the two vectors are pointing

An interpretation of this is very useful. Two vectors will form a parallelogram in space. The base of this parallelogram has length and length

77 - Matrices

Interactive Graph