Two vectors are perpendicular (or orthogonal) to each other if and only if their inner product is zero . Vectors that perpendicular to each other are also called orthogonal vectors .
When the two vectors that perpendicular to each other also have unit length (i.e. their norm is one), then these vectors are called orthonormal vectors .
The interactive program below will help you to determine whether your input vectors are orthogonal or not. When you click random example button, the program will give you a lot of examples of both orthogonal vectors and not orthogonal vectors.
Some important properties of orthogonal & orthonormal vector are
- Two unit vectors and are perpendicular to each other (orthogonal) if and only if .
In 3-dimensional Euclidean space, there are 3 standard unit vectors that orthogonal to each other with special name
. Figure below show the 3 standard orthogonal unit vectors.
The dot products of the standard orthogonal unit vector:
- Dot product of the same standard unit vector is one
- Dot product of the orthogonal standard unit vector is zero
The cross product of the standard unit vectors:
- Cross product of the same standard unit vector is zero
- Cross product of the orthogonal standard unit vector form a cycle ; ; ; ; ; ;