General settings and procedures

The applet was tested on two groups of students during the semesters of August-December 2014 and January-May 2015, each group in the first semester had 60 students while the groups in the second semester had 30 students each, making a total of 180 students. The activity to work collaboratively is about 3D Cartesian vectors containing several objectives to achieve, but the applet focuses only on three of them: a) To deduce the Pythagorean formula to calculate the magnitude of the vector given its components. b) To relate the sign of any vector component with the range of values of the corresponding direction angle. c) To deduce the relation between any component, its corresponding direction angle and the magnitude of the vector, i.e. . Although GeoGebra is used during the course for many different topics, students know very basic use of the software, so they are not required to load the applet in their own computer, although the applet was shared to them given that some students want to interact with the 3D vector themselves, but for most of the students the applet was manipulated by the instructor projecting the images in all four screens found in the classroom, prompting them to make the appropriate observations of the vector geometry. Once the applet is loaded and projected onto the screens in the classroom, it is important to describe the perspective from which the 3D system and the vector are seen, the students need to identify all three axes and their orientations in order to distinguish where the vector is located and be aware of its direction, also, any sliding to change vector components or rotation of the image to visualize different perspectives must be done slowly to avoid the students to get confused. For the objectives listed, a) and c) are eased by rotating the image in order to visualize the appropriate right triangles in a vector with all components positive, and for tasks in objective b) the components are changed to zero or negative values gradually in order to observe the possible values of the direction angles; the handling of the applet for each objective is described in the following subsections.