Conclusions

GeoGebra 5 with its 3D view offers a great potential to overcome many difficulties faced by students when learning about Cartesian 3D vectors, with the applet presented students can easily explore and discover the formula to calculate the magnitude of a 3D vector, relate the direction angles to the sign of the corresponding component and establish the mathematical relation between the latter. The applet is also used in a further session to show the projection of a vector on any of the coordinate planes, with special attention to the projection on the plane to visualize the polar angle from spherical and cylindrical coordinate vectors. An improvement to the applet would be the addition of sliders to control the values of the components rather than sliding the points on the axis were the components are drawn, also adding check boxes to hide or show the different relevant objects would allow more students to interact with the applet in their computer rather than having the instructor making the demonstration on the classroom screens.