# Two forces acting on an object produce the minimum net force if they are acting at an angle of:Multiple Choice: a) 0 degrees b) 45 degrees c) 90 degrees d) 135 degrees e) 180 degrees

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When two forces are acting simultaneously on an object then a single force their resultant forces force can be found out using the parallelogram law of forces. As per this law when two forces acting simultaneously on a particle are represented in magnitude and direction by the two adjacent sides of a parallelogram, their resultant may be represented in magnitude and direction by the diagonal of the parallelogram passing through the point.

We observe that the magnitudes of the diagonal of a parallelograms passing through a point common to two sides decreases as the angle between two sided reduces. As this angle approaches 180 degrees, the two sides tend to align along a straight line and the magnitude of diagonal tends to become equal to difference of magnitudes of two sides. Thus the resultant force is minimum when when the component forces are acting at an angle equal to 180. This amounts to the two forces acting in exactly opposite directions. Magnitude of resultant force in this case is equal to the difference of two component forces.

Therefore, option e) in the question is the right answer.

We have to deal with the additional vectorial structure called an **inner product**. In this type of additional structure each pair of vectors in the space is associated with a scalar quantity, called **the inner product of the vectors**.

In this case, the 2 forces are the 2 vectors above and if the 2 vectors are on the same dirrection but the opposite sense, the angle between 2 forces will be 180degrees, so the minimum force will be reached at 180 degrees.

Explanation:

The inner product of the resultant force is

F1*F2=IF1I*IF2I*cos (F1,F2)

Wr know that the minimum value of the

IF1I*IF2I*cos (F1,F2) is given by the minimum value of the cos (F1,F2)=-1 when the angle between F1 and F2 is 180degrees, because the rest of the product is a positive value (absolute values of the forces F1 and F2).

So the right answer is **e) 180 degrees**

The forces a and b acting on an object at an angle x has a rsulting force c given by:

c=sqrt(a^2+b^2+2abcosx)

for cosx =-1 the rsuting force c is minimum.Therefore x=180 degree or e is the correct choice.