What is the angle between two vector forces if the magnitude of resultant force is minimum?

We know that the magnitude of the resultant force vector
could be determined using the dot product of the vectors
formula.

Let the vector forces be F1 and
F2

F=F1*F2 = |F1|*|F2|*cos
(F1,F2)

Since the magnitude of the resultant force vector
is minimum, then cos (F1,F2) = -1 => F=F1*F2 =
-|F1|*|F2|

But cos (F1,F2) = -1 if the angle between the
vector forces is of 180 degrees.

Therefore,
the magnitude of the resultant force vector is minimum if the angle between the given
force vectors is of 180 degrees.