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.

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.

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.

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

UnitVector(s) yields \(\begin{pmatrix}0.6\\0.8\end{pmatrix}\).

Note Hint: In the Menu view cas.svg CAS View three-dimensional vectors and vectors with undefined variables are also valid inputs.

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

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