# crossproduct

post@engdahldata.dk shared this question 9 years ago

I have drawn two vectors u and v.

How do I make a crossproduct (or dot product) from them?

1

Hi

The dot product is just a number and you don't see it on the screen.

If the endpoint of u is at point A and the endpoint of v is at B then the dot product of u and v is

x(A)*x(B)+y(A)*y(B)

which you can type into the input line.

The cross product is a 3D vector which points at right angles to the screen so again you can't see it in 2D! The magnitude of the vector u*v is

x(A)*y(B) - x(B)*y(A)

note that swapping u and v round changes the sign in this calculation. This means that the cross product vector could be pointing straight out towards you or straight away from you. Either way, you can't see it in 2D.

It is possible to build a 3D visualisation in GeoGebra 4.0 so that you can see the cross product. No time to do this at the moment or post a link but others might?

regards

Paul

1

kondr, is there a command to use it instead of using the ⊗ simbol from the input bar?

1

Hi, in CAS you can use Cross, in GeoGebra itself it is not possible (but it is trivial to make your own tool).

1

Thank you PaulR.

I will look forward to build a 3D visualisation in GeoGebra 4.0.

But for now I will use Your suggestions.

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Do you mean a calculator like Texas TI-nSpire CAS?

Or is it something you can put into GeoGebra? -hopefully?

1

Hi

This GGB 4.0 file shows the cross product of the red vector P with the red vector S. The result is the green vector T. If P and S have z coordinate 0 (they are in the xy plane) then P crossed with S gives a vector at right angles to them both so that it points along the z axis.

Move the sliders to rotate the axes.

Change the coordinates of P and S in algebra view to see other cross products (double click, edit the numbers and press return)

regards

Paul

https://ggbm.at/553337