using animations to add a slider to a family of plots

A Maple animation automatically allows the animation to be used instead as a plot with a slider to scroll through a range of parameters of the animation parameter of the plot. These are relatively easy to create. Here is an example of projecting one vector along another, using two difference vectors from the vertices of a triangle.

fixed plot	the corresponding animatiion, see worksheet for slider application

• projectionvideo.mw This shows how to start with a fixed plot and animate it in one parameter. For the above animation, the parameter is the fraction of the opposite side difference vector (bold green vector) added to the opposite vertex position vector (blue vector). This shows a range of projections starting from an obtuse angle and finishing with acute angles.
  
• All these triangles P₁ P₂ P₃ (with edges bold green and bold black vectors) have the same height and base, and therefore the same area. This is reflected by the fact that the cross product of the green and black vectors is unchanged by adding multiples of either vector to the other. Its length is twice the triangle
  area.