Vector components in the 3 dimensions

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

untitled.jpg


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)
 
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Welcome to PF!

clickcaptain said:
I think I need to find the angles but I'm not sure how in three dimensions.)

Hi clickcaptain ! Welcome to PF! :smile:

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! :wink:
 
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?
 
clickcaptain said:
… is that right?

Yup! :biggrin:

(though I would have waited until the next step before dividing by 7 … :wink:)
then take that times the force vector given?

(you mean dot, not times, of course :wink:)

Yes … that gives you the component of force along that direction. :smile:
 
thanks! :-)
 

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