Vector Functions and Space Curves

From GeoGebraWiki

Vector equations of the form $\vec{r}(t)=(x(t),y(t),z(t))$ cannot be input directly into Geogebra, but once a coordinate system is set up and a domain for t is defined, it is possible to draw such a curve using the locus command. See 3D in Geogebra for the basic 3D setup.

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Simple Vector Equations

The helix $\vec{r}(t)=(a cos(t),a sin(t),bt)$ demonstrated at Parametric Equation of a Helix by Elisha Peterson
The toroidal spiral $\vec{r}(t)=((a+cos(bt))cos(t),(a+cos(bt))sin(t),sin(bt))$ demonstrated at Parametric Equation of a Toroidal Spiral by Elisha Peterson

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More Advanced Curves

The two worksheets below deal with the issue of when space curves intersect, or when their projections overlap.

Ballistic Equations in Three Dimensions by Elisha Peterson
Position, Velocity, and Acceleration vectors in 3D by Elisha Peterson

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Vector Functions and Space Curves

From GeoGebraWiki

Simple Vector Equations

More Advanced Curves

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