# Vector components in the 3 dimensions

1. Sep 2, 2008

### clickcaptain

Given F = (-20i + 50j = 10k)

1. The component of the foce projected along the pole AO.
2. The magnitude of the projected component of the F along the pole AO.

I have no idea where to begin, I think I need to find the angles but I'm not sure how in three dimensions.

(please excuse the picture...i know its not the greatest)

2. Sep 2, 2008

### tiny-tim

Welcome to PF!

Hi clickcaptain ! Welcome to PF!

No, you don't need to find the angles …

you're thinking of the formula F cosθ for the component of force F in a direction at an angle θ.

But you can also use the formula F.n, the direct product of the force and the unit vector in that direction …

and when the question gives you the coordinates, that's a lot easier!

3. Sep 2, 2008

### clickcaptain

so the unit vector would be ...

position vector of pole = r = 3i - 2j + 6k)
length of r = l = sqrt(3^2 + 2^2 + 6^2) = 7

u = r/l = 3/7i - 2/7 j + 6/7 k

is that right?

then take that times the force vector given?

4. Sep 2, 2008

### tiny-tim

Yup!

(though I would have waited until the next step before dividing by 7 … )
(you mean dot, not times, of course )

Yes … that gives you the component of force along that direction.

5. Sep 2, 2008

thanks!! :-)