PerpendicularVector Command

PerpendicularVector( <Line> ): Returns one of the perpendicular vector to the line.

Let Line((1, 4), (5, -3)) be the line j. PerpendicularVector(j) yields vector u=(7, 4).

The components of the perpendicular vector to a line of equation ax + by = c are (a, b).

PerpendicularVector( <Segment> ): Returns one of the perpendicular vector to the segment, having the same length.

Let Segment((3, 2), (14, 5)) be the segment k. PerpendicularVector(k) yields vector u=(-3, 11).

PerpendicularVector( <Vector> ): Returns one of the perpendicular vector to the given vector.

Let Vector((-12, 8)) be the vector u. PerpendicularVector(u) yields vector v=(-8, -12).

If a point is specified in the definition of the line, segment, or vector, the perpendicular vector will originate from that point. Otherwise, the origin will be at (0, 0).

If point A is (1, 4) and point B is (5, -3), let Line(A, B) be the line i,PerpendicularVector(i) will have its origin at A.
Let Line((1, 4), (5, -3)) be the line j. PerpendicularVector(j) will have its origin at (0, 0).

In the CAS View undefined variables are allowed as well.

PerpendicularVector((a, b)) yields the vector {-b, a}.

PerpendicularVector( <Plane> ): Creates a vector orthogonal to the plane, with starting point at (0,0,0).

PerpendicularVector(xOyPlane) yields the perpendicular vector u=(0, 0, 1) to the xOy plane.