UnitVector Command

UnitVector[ <Vector> ]

Yields a vector with length 1, which has the same direction and orientation as the given vector. The vector must be defined first.

Example:

Let v=\begin{pmatrix}3\\4\end{pmatrix}. UnitVector[v] yields \begin{pmatrix}0.6\\0.8\end{pmatrix}.

UnitVector[ <Line> ]

Yields the direction vector of the given line with length 1.

Example:

UnitVector[3x + 4y = 5] yields \begin{pmatrix}0.8\\-0.6\end{pmatrix}.

UnitVector[ <Segment> ]

Yields the direction vector of the given segment with length 1.

Example:

Let s = Segment[(1,1),(4,5)].

UnitVector[s] yields \begin{pmatrix}0.6\\0.8\end{pmatrix}.

CAS Syntax

UnitVector[ <Vector> ]

Yields a vector with length 1, which has the same direction and orientation as the given vector.

Example:

UnitVector[(a, b)] yields (\frac{a}{\sqrt{a^{2} + b^{2}}}, \frac{b}{\sqrt{a^{2} + b^{2}}}).

Example:

UnitVector[(2, 4, 4)] yields (\frac{1}{3}, \frac{2}{3}, \frac{2}{3}).