# Work and force problem with vectors

1. Jul 1, 2015

### J-dizzal

1. The problem statement, all variables and given/known data
A machine carries a 4.0 kg package from an initial position of di=0.6m$\hat i$ + 0.7m$\hat j$ + 0.26m$\hat k$ at t = 0 to a final position of df= 11.5m$\hat i$ + 14.0m$\hat j$ + 10.2m$\hat k$ at t = 15.0 s. The constant force applied by the machine on the package is F= 10.9N$\hat i$ + 13.25N$\hat j$ + 9.94N$\hat k$. For that displacement, find (a) the work done on the package by the machine's force and (b) the average power of the machine's force on the package.

2. Relevant equations
w=Fd

3. The attempt at a solution
im attempting to use the dot product here to get work but not working, i dont know why

2. Jul 1, 2015

### Scott Redmond

Quick question: should you have a vector as the result of the dot product?

3. Jul 1, 2015

never

4. Jul 1, 2015

### J-dizzal

thanks, i have been doing that lately i dont know why, i must stop doing that with the dot product.

5. Jul 1, 2015

### Nathanael

Is the j component of the initial position 0.7m or 0.75m? (You said 0.7 in the OP but I think it's a typo.)

Also what is the force supposed to be? Your OP says <10.9, 13.25, 9.94>N but your work treats the force as <5, 5, 7>N

6. Jul 1, 2015

### J-dizzal

yes your right its 0.75j for initial pos.
the force is supposed to be (5,5,7)

i made a few typos on the OP sorry Nathanael.

7. Jul 1, 2015

### Nathanael

Ok, your only mistake is miscalculating the dot product. $\vec a\cdot \vec b=a_xb_x+a_yb_y+a_zb_z$

8. Jul 2, 2015

### Scott Redmond

Ha ha.. We all do stuff like that sometimes, and it's much better to do that here than on the exam!