Like parallel forces act at the vertices , and of a triangle and are proportional to the lengths , and respectively. The center of the forces is at the
Centroid
Circum-center
Incentre
None of these
Incentre
Step 1: Formula used:
Like parallel forces act at the vertices , and of a triangle .
The forces are proportional to the lengths , respectively.
The resultant vector of some vectors is represented as,
Step 2: Calculating the position of the center of forces
Let be the forces acting at the points respectively.
Let the resultant of these forces act at a point inside the triangle.
Let be perpendicular to, perpendicular to .
The algebraic sum of the moments of the forces about = moment of the resultant about
(where denotes area of a triangle, the radius of the circle inscribed in a triangle)
The center of the force is at the incentre.
Hence option C is the correct answer.