>From the feedback I'm getting regarding curved vectors, I think it's a
bad idea, and will henceforth use the terms "curved components" and
"straight vectors"; or perhaps just let it be implied that components
may be curved or straight, and vectors will always be straight.
In any case, the length depicts the magnitude, the curvature, or lack
thereof depicts the path, and the arrowhead at the end depicts the
direction at that end point.
While "Webster's" does not define a vector as being a straight line, it
seems to be that everyone thinks of them and uses them as straight
Traditionally, force, displacement and acceleration have been depicted
as straight vectors, and the average displacement of a moving body is
the resultant of two or more vectors. Even though the resultant (a
straight vector) does not depict the actual path of the body, it has
long been considered as representing its average displacement.
Since force, displacement and acceleraion actually vary in both
magnitude, and direction, they can best be depicted with curved
components; all drawn to scale:
The initial velocity of an object can be depicted with a straight
vector, oriented in a convenient, arbitrary direction from a point of
beginning, and its actual resultant path - the evolute - can be
depicted as the arc of an ellipse, also from that same point of
The displacement, or displacements will emanate - as an involuted curve
- from a point or points along a straight tangent that is aligned with
the initial velocity vector to points on the resultant arc that are
equadistant from the point of beginning.
These three components form a geometric figure with three sides - two
curved and one tangent - and three angles: an apex angle with two right
angles opposite it. The shape of this figure remains the same
regardless of its size and extent.