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

justaguide | College Teacher | (Level 2) Distinguished Educator

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For the magnitude of the resultant of two forces to be minimum, the angle between the two vectors that represent the forces should be 180 degrees. In other words the forces should be in the opposite direction.

If the forces are F1 and F2, the magnitude of the resultant force when the angle between the vectors representing the forces is 180 degrees, is equal to |F1 - F2|.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.