CAS 3D Vector commands

Which operations would you like?

CAS requests:

These things would simplify the handling and understandling for pupils:

1) small letters should automatically create a vector object: a:=(1,2,3) or ab:=(3,4,3) whereas A:=(3,2,1) should create a Point object

2) vectors should be displayed in columns (as well in 3d-line objects in the algebra window)

These operations / commands I'd like to use with 3d vectors (some of them are included yet, but do not function without problems under various conditions)

1) Vector[ <Start Point>, <End Point> ]

2) Line[ <Point>, <Vector> ]

3) Angle[ <Vector>, <Vector> ]

4) Distance[ <Point>, <Object> ]

5) Length[<Vector>] functions, but is not displayed as a possible command

6) sometimes even these simple operations lead to an error message for various reasons

vector+vector; vector - vector; number*vector

7) these function well: Dot[ <Vector>, <Vector> ]

Cross[ <Vector>, <Vector> ]

Solve[ vector equation]

Substitute[vector equation]

Greetings from Germany

Jan

Please try 5.0.26.0 for some first steps.

For now, rather than

u+v

a:=(1,2)

you need to write

Vector[u+v]

a:=Vector[(1,2)]

and vectors aren't displayed as column vectors yet.

Some examples of what's working:

Vector[(1,2)]

Vector[(1,2,3)]

Vector[(1,2), (5,7)]

Length(Vector((1,2)))

Length(Vector((1,2,3)))

5*Vector((1,2))

5*Vector((1,2,3))

Vector((1,2)) / 5

Vector((1,2,3)) / 5

Vector[(1,2)] * Vector[(3,4)]

Vector[(1,2)] * Vector[(3,4,5)]

Vector[(1,2,3)] * Vector[(4,5)]

Vector[(1,2,3)] * Vector[(4,5,6)]

Cross[Vector[(1,2)], Vector[(3,4)]]

Cross[Vector[(1,2,3)], Vector[(4,5)]]

Cross[Vector[(1,2)], Vector[(3,4,5)]]

Cross[Vector[(1,2,3)], Vector[(4,5,6)]]"

Line[(1, 2), Vector[(3, 4)]]

Angle[Vector[(1,2)], Vector[(3,4)]]

Angle[Vector[(1,2,3)], Vector[(4,5)]]

Angle[Vector[(1,2,3)], Vector[(4,5,6)]]

x(Vector[(1,2,3)])

y(Vector[(1,2,3)])

z(Vector[(1,2,3)])

x(Vector[(1,2)])

y(Vector[(1,2)])

Dot[Vector[(a,b)],Vector[(c,d)]]

Vector[1,2]

Vector[Vector[(1,2)] + Vector[(3,4)]]

Vector[Vector[(1,2)] + Vector[(3,4,5)]]

Vector[Vector[(1,2,3)] + Vector[(4,5)]]

Vector[Vector[(1,2,3)] + Vector[(4,5,6)]]

Vector[(1,2)+(3,4)]

Vector[(1,2,3)+(4,5,6)]

abs(Vector((1,2)))

abs(Vector((1,2,3)))

As you shurely recognized, I'm teaching calculating with vectors and GeoGebra this semester.

So my pupils and me are thankful for the quick implementing of our wishes.

While experimenting I found something strange in my oppinion.

I'm not shure whether this is the right place to post it, but I'll try it here:

Angle[Vector[a],Vector] is OK in 5.0.26.

But why leads Angle[a,b] to an error message, even if a and b are defined as vectors (a:=Vector[(1,2,3)] and b:=Vector[(4,5,6)]) before?

this worked well in 5.0.19. :-(

It looks like Angle[ u, v ], where u and v are defined as vectors now works.

It would be nice if, as an example;

Angle[ (1,0,0), (2,-3,5) ]

also would work.

If using Points, you need to specify 3 (as in the Input Bar) ie

Angle[ (1,0,0), (0,0,0),(2,-3,5) ]

or specify Vectors

Angle[ Vector[(1,0,0)],Vector[(2,-3,5)] ]

Yes, that is what we don't like :-)

As there is no command "Angle[ <point>,<point>]", there should be no ambiguity and possible

to interpret

Angle[ (1,0,0), (2,-3,5) ]

as a command to find the angle between the two vectors.

(It appears to confuse both pupils and Teachers that this vector operation behaves

differently from Dot[ (1,0,0),(2,-3,5)] )

Please try 5.0.49.0, online now. Some really nice improvements:

* a:=(1,2) works to define a vector

* vectors are displayed as column vectors

* Angle[(1,2),(3,4)] works :)

Great work!!! Thanks!!!

There are some more things, that should be fixed or included:

1. Some operations with vectors work fine and the results are displayed as vectors:

these are defined:

d:=(2,3,1)

e:=(g,3,1)

results are displayed in columns:

Cross[d, e]

d+2*e

results are not displayed in columns:

d⊗e

Cross[e, d]+d

2. I wonder if the line-objects in algebra and CAS-module are compatible?

In the algebra-mode there is λ the parameter.

In the CAS-module the command t:=Line[(2,1,2),(2,1,4)] leads to t as a parameter even

if the line itself is named like that.

It would be helpful, if lines in CAS-module are displayed in columns as well as

separated in vector + parameter* vector like in algebra-mode and if the parameter

would be handled equal. Perhaps λ, λ_1, λ_2, ... could be reservated?

Merry christmas from Germany

Jan

Please try 5.0.53.0 - I think all the problems in (1) are fixed