Cross Product in Geogebra

In this tutorial, I'll guide you through calculating the cross product of two vectors using Geogebra.

Begin by creating two vectors in a three-dimensional space.

The coordinates for the first vector are

$$ \vec{v} = \begin{pmatrix} 1 \\ 2 \\ 1 \end{pmatrix} $$

And for the second vector,

$$ \vec{u} = \begin{pmatrix} -2 \\ -1 \\ 1 \end{pmatrix} $$

If you're not sure how to create a vector, refer to our online lesson on crafting vectors with Geogebra.

Next, input Cross(v,u) into Geogebra's command field and hit enter.

Here, u and v refer to the names of the vectors you've just crafted.

Geogebra will then compute and illustrate the cross product of your vectors.

For this example, the resulting cross product is vector w, with coordinates as follows.

$$ \vec{u} = \begin{pmatrix} 3 \\ -3 \\ 3 \end{pmatrix} $$

Why is the cross product important? The cross product between two vectors u and v results in a third vector w. This vector is distinctively positioned perpendicular to the original pair. The orientation of this resultant vector is determined by the sequence of the original vectors. If the initial vectors align in the same direction, the outcome is a null vector. The magnitude of the cross product reflects the area encompassed by the two vectors on their mutual plane.

If you're enjoying this hands-on guide from StemKB, stay tuned for more.