This Demonstration shows the decomposition of a vector in 3D. The components of the three vectors , , and defining the directions of decomposition and of the vector to be decomposed are adjusted using the sliders. The scalar multipliers , , of each of the three vectors are calculated and the prism defining the decomposition is graphed.
The scalar multipliers , , are obtained by solving a linear system having an augmented matrix with columns defined by the components of , , , and . If the determinant of the system is zero, corresponding to , , and being linearly dependent, a message is displayed prompting the user to make another selection.