By Kardi Teknomo, PhD .
LinearAlgebra

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Two vectors are perpendicular (or orthogonal) to each other if and only if their inner product is zero Orthogonal Vector . 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 Orthogonal Vector and Orthogonal Vector are perpendicular to each other (orthogonal) if and only if Orthogonal Vector .
  • In 3-dimensional Euclidean space, there are 3 standard unit vectors that orthogonal to each other with special name Orthogonal Vector , Orthogonal Vector and Orthogonal Vector . Figure below show the 3 standard orthogonal unit vectors.
    Orthogonal Vector
  • The dot products of the standard orthogonal unit vector:
    • Dot product of the same standard unit vector is one Orthogonal Vector
    • Dot product of the orthogonal standard unit vector is zero Orthogonal Vector
  • The cross product of the standard unit vectors:
    • Cross product of the same standard unit vector is zero Orthogonal Vector
    • Cross product of the orthogonal standard unit vector form a cycle Orthogonal Vector ; Orthogonal Vector ; Orthogonal Vector ; Orthogonal Vector ; Orthogonal Vector ; Orthogonal Vector ;

See also : dot product , cross product , vector norm

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