For example, assume you’re looking for a hotel that’s 20 miles due east and then 20 miles due north. And to find you use the inverse tangent function (or inverse sine or cosine). To find the magnitude, you use the Pythagorean theorem.

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. In physics, sometimes you have to find the angle and magnitude of a vector rather than the components.

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.

Magnitude of a 3d vector