If anyone uses the graphing software Grapher on the Mac, I could use some help. Specifically, there are four things I want to do that I couldn't figure out:
1) How do you restrict the "domain" of a graph? For example, how do you graph $y=x+1$ (in 3 space) with the restriction $z=2$? Or a combination of conditions like $4<x<10$ and $1 \leq y \leq 5$?
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 appreciated!