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

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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's profile pic

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.

We’ve answered 333,966 questions. We can answer yours, too.

Ask a question