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Vectors for a plane watch

1. a plane has cartesian eqn: x+2y+3z=4
a force acts on the plane where F=2i - j + k the units of F are Newtons

Find the component of F normal to the plane.

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Would I calculate the cross product of F with the vector form of the equation for the plane, and this would give me the normal vector which is F isn't it?

BUT I'm unsure how to convert the cartesian form for the plane to a vector form

2. (Original post by DonnieBrasco)
You don't need to work out the vector form of the plane.

Just note that if the plane has equation x+2y+3z=4, then i+2j+3k is a normal vector.

And you want to utilise a function of the dot product, rather than vector product.
3. Essentially you are required to discover the projection vector of the force F onto the normal to the plane given.

Peace.
4. if i recall correctly you can do F.nu where nu is the unit vector in the direction of the normal to obtain the magnitude of the component. Then multiply that by nu to get the vector component.
5. (Original post by the bear)
if i recall correctly you can do F.nu where nu is the unit vector in the direction of the normal to obtain the magnitude of the component. Then multiply that by nu to get the vector component.
Absolutely correct.

F.nu gives the length of projection of the force F onto the normal to the plane. So do remember to append nu at the back of the resulting scalar product to arrive at the required vector.

Hope it helps. Peace.
6. OK so the unit vector of n is (1,2,3)/root(14) and you're saying that I dot product this with the vector F which gives (1,2,3)/root(14) . (1,2,3) = root(14)

now where do I go? Sorry I'm being a bit slow, not very good with vectors
7. (Original post by DonnieBrasco)
OK so the unit vector of n is (1,2,3)/root(14) and you're saying that I dot product this with the vector F which gives (1,2,3)/root(14) . (1,2,3) = root(14)

now where do I go? Sorry I'm being a bit slow, not very good with vectors
Check what you've done. You haven't dotted it with F.

When you've done that, this becomes the scaler for the unit vector in the direciton of the normal
8. Ahh yes, silly mistake. (1,2,3)/root(14) . (2,-1,1) = 3/root(14), so are you saying that this is the component of the force normal to the plane?
9. (Original post by DonnieBrasco)
Ahh yes, silly mistake. (1,2,3)/root(14) . (2,-1,1) = 3/root(14), so are you saying that this is the component of the force normal to the plane?
This is the magnitude of the component, and will be the multiplier of the unit normal vector.

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Updated: March 29, 2013
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