A 3D VIRTUAL LAB ON VECTOR OPERATIONS AND THEIR PROPERTIES

In Physics, a big number of quantities are vectors, and their use requires typical operations such as: addition, substraction, scalar multiplication, scalar product (dot product), vector product (cross product) and scalar triple product. This is a very basic topic in all General Physics courses for Engineering degrees. However, we have detected that some students lack of a deep understanding of vector operations and their properties.

In this work, we present a virtual laboratory (developed using the tool “Easy Java Simulations”) for the study and understanding of vector operations and their properties. The user can introduce the components of the input vectors and gets a 3D representation, which can be scaled and rotated for a better visualization. Any of the aforementioned operations can be selected, and the result is shown both numerically and graphically.

The user can also modify any represented vector by dragging its tip with the mouse. In this way, the virtual lab provides a real time visualization of how the change affects the result. The possibility of limiting the changes to either magnitude or direction is also included.

The virtual lab includes options for copy and paste vectors and results. That enables the user to verify different properties of some vector operations (commutative, distributive). Geometrical properties (scalar product of vector and unit vector, magnitude of vector product, absolute value of scalar triple product) can be understood by means of the adequate representation (projection in a given direction, parallelogram, parallelepiped).
Note: The Java laboratory (in Spanish) can be seen at http://labvirtual.webs.upv.es/Vectores.html. HTML5 version (in English) will be available before Congress.