JEE Main · 2007 · 29 Apr 2007 · Offline · Vector Algebra

The resultant of two forces

P N

and

3 N

is a force of

7 N

. If the direction of

3 N

force were reversed, the resultant would be

19 N

. The value of

P

Answer: (A)

Solution

Let

θ

be the angle between the forces. The resultant of

P

and

3

N gives

49 = P^{2} + 9 + 6 P cos θ

, while reversing the

3

N force gives

19 = P^{2} + 9 - 6 P cos θ

. Adding the two equations removes the cosine term and leaves

68 = 2 P^{2} + 18

, so

P^{2} = 25

and

P = 5

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option