## Orthogonal Vector

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.

vector x vector y

## Properties

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 , and . 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 ; ; ; ; ; ;

See also : dot product , cross product , vector norm