A 14 N force with a fixed orientation does work on a particle as the particle moves through displacement d = (2i - 4j + 3k) m. What is the angle between the force and the displacement if the change in the particle's kinetic energy is (a) +7.54 J and (b) -7.54 J?

Answer 1

The scalar "dot" product of the Force F and the displacement d,
F*d = |F||d| cos theta.
equals the work done, which equals the kinetic energy increase.

Use that fact to compute the cosine of theta, the angle between the two vectors.

The magnitude of F, represented by |F|, is 14N.

The magnitude of d is sqrt29 = 5.39 m

Answer 2

f*d=fd