physics
posted by sel .
(a)At a certain instant, a particlelike object is acted on by a force F = (4.0 N)i  (2.0 N)j + (9.0 N)k while the object's velocity is v =  (2.0 m/s)i + (4.0 m/s)k . What is the instantaneous rate at which the force does work on the object?
(b)At some other time, the velocity consists of only a j component. If the force is unchanged, and the instantaneous power is 12 W, what is the velocity of the object just then?

work=force dot dx
the dot product is scalar, so all the components (ii,jj,kk) are added.
b) power= d work/dt= d Force dot velocity/dt
12watts= (4i2j+9k) vj
vj= 12/2 = 6j