Three non-parallel coplanar forces which can be represented both in magnitude and direction by the three sides of a triangle taken in order will

Analyze the question

The question is about the triangle law of forces. It asks what happens when three non-parallel coplanar forces can be represented in magnitude and direction by the three sides of a triangle taken in order.

Concept

The triangle of forces states that if three forces acting at a point can be represented in magnitude and direction by the three sides of a triangle taken in order, the forces are in equilibrium.

Taken in order means head-to-tail. The resultant of the vector sum is zero, because you return to the starting point.

Solution

1. Let the forces be F₁, F₂ and F₃, drawn head-to-tail to form a closed triangle.
2. The closed triangle means F₁ + F₂ + F₃ = 0.
3. Rearranging gives F₃ = −(F₁ + F₂).
4. This means F₃ is equal in magnitude and opposite in direction to the resultant of F₁ and F₂. In other words, F₃ is the equilibrant of F₁ and F₂. The same reasoning applies to any one of the three forces.

Checking the options

• A. Any one force is the equilibrant of the other two. This is correct, as shown above.
• B. Random motion. Incorrect, since the net force is zero.
• C. Oscillation. Incorrect.
• D. Moving along a straight line. This would need a net force, but the net force here is zero. A body in equilibrium either stays at rest or moves at constant velocity, so this is not the best answer.
• E. Rotation about an axis. Incorrect. Forces that meet at a point and are in equilibrium produce no net turning effect.

Answer: A

Tip: "Triangle closed means forces balanced." If vectors form a closed polygon head-to-tail, the resultant is zero, so the body is in equilibrium. Any one force then equals the equilibrant of the rest.