In this example, three of the four dimensional quantities are fundamental units, so the last (which is g ) must be a combination of the previous. Note that if a 2 (the coefficient of M ) had been non-zero then there would be no way to cancel the M value; therefore a 2 must be zero. Dimensional analysis has allowed us to conclude that the period of the pendulum is not a function of its mass M . (In the 3D space of powers of mass, time, and distance, we can say that the vector for mass is linearly independent from the vectors for the three other variables. Up to a scaling factor, g → → + 2 T → → − − L → → is the only nontrivial way to construct a vector of a dimensionless parameter.)