Maple Student packages are designed explicitly for teaching and learning concepts in mathematics. In Maple 17, the student package for multivariate calculus has been expanded to provide more tools for exploring problems involving lines and planes.
For many applications, the lines and planes that the objects represent will be fully determined. However, Maple supports arbitrary algebraic expressions occurring in the coordinates of the parameters used to define the objects. For example, it can handle the line through the points
We construct two lines; the first contains the point [1, 0, 2]; and the direction `<,>`(2, -2, 1);, the second the points [5, -3, 1]; and [3, -3, 6];. The Line and Plane objects understand lists as points and Vectors as directions.
Let us see if
The intersection is a point.
We can also find
We can obtain various other representations of a line with the GetRepresentation command.
We construct a third line, parallel to
What is the relative position of
We can compute the (Euclidean) distance between a pair of lines using the Distance command. Intersecting lines are at distance 0.
The GetPlot command shows a visualization of the line.
In order to combine visualizations, one can use plots:-display. With all features of the visualizations turned on, it is a little crowded, so we turn some of them off.
Let's consider the plane containing
What is the relative position of
The distance between Since
Now let us consider a family of lines. We let
If we can find values for
We now let
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