This page explains how to plot the intersections between two or more graphs in Graphing Calculator 3D.
Steps:
Plot two or more equations in 3D.
Pick the equation you wish to plot intersections for. (The intersection between this equation and all other equations that are currently plotted will be drawn)
From "Draw" combo-box select "Intersection".
[Optional] Click on the color box to select a color for your intersection lines.
[Optional] Drag the Thickness slider to increase or decrease the thickness of contour lines.
[Optional] Select Transparency and drag its slider to left in order to hide everything except the intersection lines.