Intersect a plane and a line in the [img]https://wiki.geogebra.org/uploads/thumb/b/bb/Perspectives_algebra_3Dgraphics.svg/16px-Perspectives_algebra_3Dgraphics.svg.png[/img] [i]3D Graphics View[/i] of [i]GeoGebra [/i]to create the intersection point.

Drag the points [i]A [/i]and [i]B[/i] and explore how the position of the intersection point changes.

[table][tr][td][size=100]1.[/size][/td][td][size=100][/size][/td][td][size=100]Enter p: x + y = z into the [i]Input Bar[/i] in the [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] and hit the [i]Enter [/i]key to define a plane [i]p[/i].[br][/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][size=100][/size][/td][td][size=100]Create two points [i]A[/i] and [i]B[/i] by entering A = (3, 4, 3) and B = (-4, -2, -1) into the [i]Input Bar[/i] and hitting the [i]Enter[/i] key after each input.[/size][/td][/tr][tr][td][size=100]3.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_join.png[/icon][/size][/td][td][size=100]Select the [i]Line[/i] tool from the [i]3D Graphics Toolbar[/i] and click on the points [i]A [/i]and [i]B[/i] respectively to create the line [i]a[/i] through both points.[/size][/td][/tr][tr][td][size=100]4.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon][/size][/td][td][size=100]Select the[i] Intersect[/i] tool. Then, click on the plane and the line to create the intersection point [i]C[/i].[/size][/td][/tr][tr][td][size=100]5.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/size][/td][td][size=100]Use the [i]Move [/i]tool to change the position of the points [i]A[/i] and [i]B[/i]. What happens to the intersection point if the line is parallel to the plane, or if both points lie within the plane?[/size][/td][/tr][tr][td][br][/td][td][br][/td][td][size=100][b]Hint:[/b] By clicking on a point you can switch between moving the point parallel to the [i]x[/i]-[i]y[/i]-plane or parallel to the [i]z[/i]-axis.[/size][br][/td][/tr][/table]