How to Find Intersection in GeoGebra

You can quickly find intersections between lines, planes and spheres in GeoGebra using the following sets of instructions.

GeoGebra Instruction 1

1.: Open 3D Graphics and Algebra View under View in Menu.
2.: Add the two objects that you want to intersect by entering them into Algebra View. If one or both of your objects are lines, then they must be added by using one of the Line commands.
3.: Enter

Intersect(<object>, <object>)

and fill in the names of the objects as they appear in Algebra View.
4.: The intersection points or lines are now shown in Graphics View and Algebra View.

Example 1

Enter the equation of the sphere

{(x - 2)}^{2} + {(y - 1)}^{2} + z^{2} = 64

in Algebra View. Create a line with the command Line(<point>, <direction vector>). Choose $(- 2, 1, 0)$ as the point on the line, and $(1, 1, 1)$ as the direction vector of the line. Then, use the command

Intersect(<object>, <object>)

to find where the line intersects the sphere.

Screenshot of GeoGebra showing a line passing through a sphere

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