Google ClassroomGoogle Classroom
GeoGebraGeoGebra Classroom

Vector Scalar Triple Product

The applet below illustrates a vector triple product. In statics the vector triple product can be used to calculate the moment from a force at a point C about an axis AB. where: is a unit vector directed from point A to Point B is the force vector at point C is the position of the force vector at C relative to any point on the line AB The scalar vector triple product is also the volume of a parallel-piped formed from the three vectors. Shown below is a parallel-piped formed from three vectors P, Q and S. Also shown is another parallel-piped formed with P replaced by a vector shifted by a factor times the Q and a factor times the S vectors. The vector, Pnew, is in a plane parallel to the plane formed by the Q and S vectors. Changing the view and shift amounts you should see the new shape is a skewed version of the original shape and should have the same volume. This is equivalent to shifting the top of a parallelogram where the height remains constant.