By Kardi Teknomo, PhD .
LinearAlgebra

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A unit vector is a vector of unit length . Any non-zero vector can be normalized into a unit vector by a division of a vector by its norm, that is Unit Vector .
Note that unit vector is not equal to one vector Unit Vector , it is the magnitude of the vector is one, not the elements.

Example:
Suppose we have vector Unit Vector
The norm of the vector is Unit Vector
Converting it to unit vector becomes Unit Vector
Now the norm of the unit vector is Unit Vector



The interactive program below will help you to convert your vector input into a unit vector of any positive dimension. The program will also show you the norm of input vector, norm of unit vector (which is always 1) and sum of the unit vector.


Report in rational format

Properties

Some important properties of unit vector are

  • The inner product of a unit vector to itself is one Unit Vector .
  • Two unit vectors Unit Vector and Unit Vector are perpendicular to each other (orthogonal) if and only if Unit Vector .
  • In an Euclidean space, the standard unit vectors that orthogonal to each other has name:
    • unit vector of the first dimension is Unit Vector
    • unit vector of the second dimension is Unit Vector
    • unit vector of the third dimension is Unit Vector
    Unit Vector



  • The dot products of the standard unit vector:
    • Dot product of the same standard unit vector is one Unit Vector
    • Dot product of the perpendicular standard unit vector is zero Unit Vector
  • The cross product of the standard unit vectors:
    • Cross product of the same standard unit vector is zero Unit Vector
    • Cross product of the perpendicular standard unit vector form a cycle Unit Vector ; Unit Vector ; Unit Vector ; Unit Vector ; Unit Vector ; Unit Vector

See also : dot product , cross product , vector norm , basis vector

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