Two forces, F 1 and F 2 , act on a particle. F 1 = 2i

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Two forces, F1 and F2, act on a particle.

F1 = 2i − 5j newtons

F2 = i + j newtons

The resultant force R acting on the particle is given by R = F1 + F2.

a. Calculate the magnitude of R in newtons. A third force, F3 begins to act on the particle, where F3 = kj newtons and k is a positive constant. The new resultant force is given by Rnew = F1 + F2 + F3.

b. Given that the angle between the line of action of Rnew and the vector i is 45 degrees, find the value of k.

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