# Deducing Magnitude and Direction Cosines of a 3D Vector

- Topic:
- Cosine

Students in an introductory college physics course are prompted to solve a cooperative worksheet about 3D cartesian vectors, some of the objectives of such activity are: a) to deduce the equation 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, and c) to deduce the relation between any component, its corresponding direction angle and the magnitude of the vector, i.e. . In order to aid students in this guided activity, a GeoGebra applet was built in which the components of a 3D vector can be set easily by sliding points on the axes to observe the appropriate relationships. This construction has been tested in four groups making a total of 180 students and it was observed that more than 70% of them were able to deduce correctly most of the relations with little or no further aid than the instructor's demonstration of the applet, compared to historical sessions without the use of GeoGebra in which very few of the students were able to deduce the correct results without frequent aid from the instructor or were not able to complete the activity in the 80-minute session.