Physics · Laws Of Motion · NEET
Only if they point in exactly the same direction. Force is a vector, so 3 N and 4 N give 7 N only when they are parallel. If they are at an angle you must use vector addition. For example, 3 N and 4 N acting at 90 degrees give a resultant of 5 N, not 7 N, because R = square root of (3^2 + 4^2) = 5 N.
If two forces acting on a body are represented in size and direction by two sides of a triangle taken in order (head of the first touches the tail of the second), then the third side taken in the opposite order gives their resultant in size and direction. It is just head-to-tail vector addition drawn as a triangle.
They give the same resultant; only the drawing differs. In the triangle law you place the two force arrows head-to-tail. In the parallelogram law you place them tail-to-tail and complete a parallelogram, so the diagonal is the resultant. The parallelogram law gives the handy formula R = square root of (P^2 + Q^2 + 2PQ cos theta).
Taken in order means each force starts where the previous one ended, so the arrows follow around the shape one after another. If three forces form a closed triangle (the last arrow ends exactly at the start of the first), their vector sum is zero. Zero net force means zero acceleration, so the body's velocity does not change. This exact idea was asked in NEET 2019.
When two forces P and Q are at 90 degrees, cos 90 = 0, so the formula reduces to R = square root of (P^2 + Q^2). The direction is set by tan alpha = Q / P from the force P. The full acceleration version of this is covered in the next concept, Acceleration from Two Perpendicular Forces.
The resultant is zero when the force vectors, drawn head-to-tail, form a closed figure (a closed triangle for three forces, a closed polygon for more). Zero resultant means the particle is in equilibrium: it stays at rest or keeps moving with constant velocity.
A particle moving with velocity V is acted upon by three forces represented by the sides of a triangle PQR (taken in order). The velocity of the particle will:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is the single force that has the same effect as the two forces acting together. It is found by vector addition, using the triangle law or the parallelogram law, not by simple arithmetic unless the forces are parallel.
R = square root of (P^2 + Q^2 + 2PQ cos theta), where P and Q are the two force magnitudes and theta is the angle between them. The direction is given by tan alpha = (Q sin theta) / (P + Q cos theta).
The maximum is (P + Q) when the forces point the same way (theta = 0). The minimum is |P - Q| when they point in opposite directions (theta = 180 degrees). Any resultant between these two values is possible.
NEET often tests whether forces forming a closed triangle give zero net force and constant velocity (as in 2019), and it is the base idea for equilibrium of a particle and for combining perpendicular forces. Getting vector addition right prevents easy calculation traps.
Yes. Both are vectors, so both follow the same triangle and parallelogram laws of head-to-tail addition. Any physical quantity that is a vector obeys these rules.
