1) Three vectors are coplanar if one can be expressed as a linear combination of the other two.
2) Three vectors ,
are coplanar if the points A, B, C and D are in the same plane
This scalar triple product can also be understood as the determinant of the 3x3 matrix having the three vectors as its rows and columns (the determinant of a transposed matrix is the same as the original); this quantity is invariant under coordinate rotation.