JEE Main & Advanced Mathematics Statistics Parallel Forces

(1) Like parallel forces : Two parallel forces are said to be like parallel forces when they act in the same direction.

The resultant \[R\] of two like parallel forces \[P\] and \[Q\] is equal in magnitude of the sum of the magnitudes of forces and \[R\] acts in the same direction as the forces \[P\] and \[Q\] and at the point on the line segment joining the point of action \[P\] and \[Q,\] which divides it in the ratio \[Q:P\] internally.

(2) Two unlike parallel forces : Two parallel forces are said to be unlike if they act in opposite directions.

If \[P\] and \[Q\] be two unlike parallel forces acting at \[A\] and \[B\] and \[P\] is greater in magnitude than \[Q\]. Then their resultant \[R\] acts in the same direction as \[P\] and acts at a  point \[C\] on \[BA\] produced. Such that \[R=P-Q\] and \[P.CA=Q.CB\]

Then in this case \[C\] divides \[BA\] externally in the inverse ratio of the forces, \[\frac{P}{CB}=\frac{Q}{CA}=\frac{P-Q}{CB-CA}=\frac{R}{AB}\].