Unit vector facts for kids

Kids Encyclopedia Facts

A unit vector is any vector that is one unit in length. Unit vectors are often notated the same way as normal vectors, but with a mark over the letter (e.g. $a-hat$ being the unit vector of $a-hat$ .)

To make a vector into a unit vector, one just needs to divide it by its length: $\hat{\mathbf{v}} = \mathbf{v} / \lVert \mathbf{v} \rVert$ . The resulting unit vector will be in the same direction as the original vector.

In component form

Three common unit vectors used in component form are $i-hat$ , $j-hat$ and $k-hat$ , referring to the three-dimensional unit vectors for the x-, y- and z-axes, respectively. They are commonly just notated as i, j and k.

They can be written as follows: $Components i,j and k$

For the unit vector corresponding to the $i$ -th basis vector of a vector space, the symbol $e_i$ (or $\hat{e}_i$ ) may be used.

Euclidean vector

Unit vector facts for kids

In component form

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See also