Vectors in physics

Question

need solution for 41st  question

The greater and least resultant of two forces are 7N and 3N respectively. If each of the force is increased by 3N and applied at 60 degree. The magnitude of the resultant is

Answer 1

Let the two forces be x and y

Greatest resultant ( parallel cosz=1) = x+y = 7N ------------(1)

Least Resultant ( antiparallel cosz= -1) = x-y = 3N -------------(2)

Solving equation (1) and (2) we get  x =5N, y =2N

Each force is increased by 3N

Therefore x = 8N, y = 5N

Resultant vector = ( x² + y² +2xycos60^o)^1/2

= (64 + 25 + 2*8*5*1/2)^1/2

= √129