questions about vectors and graphing in Grapher

I am a new user of Grapher, and there doesn't seem to be a user manual for the program. So I'm hoping someone can help me with four issues I've had:

1) How do I make the axes all different colors in a 3-D graph? I want the x-axis to be red, the y-axis to be green, and the z-axis to be blue, but I haven't figured out how.

2) How do I plot a vector? When I choose the vector option from the palette and fill in values for x and y, Grapher just plots a point. But I want Grapher to graph the actual vector, an arrow starting at the origin and ending at the point.

3) Grapher seems to graph vector fields incorrectly. For example, I wanted to plot the 2D vector field -yi + xj. So I did Equation -> New Equation from Template -> Vector Field, and chose Explicit Cartesian. In the top blank space of the empty vector I filled in -y, and in the bottom blank space I filled in x. Grapher then produced a vector field with the correct shape, but all of the vectors were the same length. This is incorrect, as the arrows should get longer the farther they are from the origin. Am I doing something wrong, or does Grapher just not handle vector fields correctly? I did notice that as you move farther away from the origin, the vectors change color, so is color change just how Grapher shows that the vectors are getting longer? If so, how do I change it to display the actual length of the vectors?

4) Can Grapher do dot product and cross product of vectors? Can I hand Grapher two 3-D vectors, and have Grapher spit out the resulting cross product (and simultaneously graph all three vectors)?

Any help will be greatly appreciated!

Hi !
A 83 pages manual (French and English) can be downloaded (free and free of advertising) on this website : <http://y.barois.free.fr/grapher/> A lot more documentation about Grapher.app and various works "made in Grapher" on this site.
Enjoy,
YB24

Bonjour Strangelove1221,
Quick replies to your questions :
1) menu Format > Axes & Frame > select an axis > OK then Inspector and choose color and so on.
2) Grapher can plot a vector field 2D or 3D, a line segment defined by two points but without an arrow, using equations.
If you want a vector as an arrow on a 2D graph : menu Object > Insert Arrow > select it in the Graph, adjust place, size, use Inspector.
A better way (2D only) : use a point set, defined the two points (origin & end) of the vector, open the Inspector that allows none, one or two arrows on these points.
3) Vector fields are exact when defined in cartesian coordinates but approximate with other coordinate systems (see the 83 pages Instructions for Use-Grapher pages 38-40 on the website shown in the previous post).
Vector length : select the vector field equation, open the Inspector and check Proportional and adjust size. After changing Density, click the circular arrow near «*high*».
4) Grapher does not compute product nor cross products of vectors («*produit scalaire*» and «*produit vectoriel*» in French). Grapher can graph only equations and compute algebraic expressions.
So long,
YB24