Calculating the Angle Between a Force and Displacement

[TomFoolery]

Homework Statement

A 13 N force with a fixed orientation does work on a particle as the particle moves through displacement = (3i - 5j + 3k) m. What is the angle between the force and the displacement if the change in the particle's kinetic energy is (a) +25.6 J and (b) -25.6 J?

Homework Equations

Angle = √(x^2 + y^2 + z^2)
Work = mad or F (dot) d

The Attempt at a Solution

I'm not sure how to approach this. I know that the dot product really just means to multiply the x parts by x parts, y parts by y parts, and z parts by z parts (or $\hat{i}$, $\hat{j}$, and $\hat{k}$ parts, if you prefer).

If the particle starts at (0, 0, 0), then the force would have caused it to go to its current position (3, -5, 3). I'm still not sure that is what is being said though.

 

[SammyS]

There is another way to express the dot product, $\vec{F}\cdot\vec{d}\,.$

It involves the magnitude of each of the vectors as well as the cosine of the angle between their directions.

 

[kjohnson]

Yes, work is equal to Fx*dx+Fy*dy+Fz*dz where where Fx,Fy,Fz are the force components and dx,dy,dz are the displacement components...but there is another common way to write the the dot product of two vectors that should make quick work of this problem.

 

[TomFoolery]

Got it, thanks for your help.