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}.

Hint: In the CAS View three-dimensional vectors and vectors with undefined variables are also valid inputs.

Examples:

• UnitVector((a, b)) yields (\frac{a}{\sqrt{a a + b b}}, \frac{b}{\sqrt{a a + b b}}).
• UnitVector((2, 4, 4)) yields (\frac{1}{3}, \frac{2}{3}, \frac{2}{3}).