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Vectors and the dot product

Hey guys, any ideas on how I would solve the attached questions, the dot product one is the most problematic. Thanks a lot!
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Original post by MFAHH
Hey guys, any ideas on how I would solve the attached questions, the dot product one is the most problematic. Thanks a lot!


Note that the question says "Show that". This means that all you need do is substitute the given value of x into the original equation and "show that" it satisfies it. It does work. Remember that a.b=b.a
Original post by MFAHH
Hey guys, any ideas on how I would solve the attached questions, the dot product one is the most problematic. Thanks a lot!


For the second one, what have you done so far? Can you post your diagram showing ALL forces?
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MFAHH
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Original post by brianeverit
Note that the question says "Show that". This means that all you need do is substitute the given value of x into the original equation and "show that" it satisfies it. It does work. Remember that a.b=b.a


Thanks for the reply. What of the hinted method specifically, i.e. by taking the scalar product with vector b? I'm puzzled as to how to do that, and as it happens, I'm meant to solve a set of questions using the same method later on in my assignment.

Original post by brianeverit
For the second one, what have you done so far? Can you post your diagram showing ALL forces?


I've attached what I've got so far. I know; it's not much. I can't seem to think where to go from there. I'm also not sure on my positioning of the x and y axes.


20140203_163638.jpg510.7KB
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davros
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Original post by MFAHH
Thanks for the reply. What of the hinted method specifically, i.e. by taking the scalar product with vector b? I'm puzzled as to how to do that, and as it happens, I'm meant to solve a set of questions using the same method later on in my assignment.



Well, what do you get if you do what the question suggests and take the dot product of the original equation with vector b?
Original post by MFAHH
Thanks for the reply. What of the hinted method specifically, i.e. by taking the scalar product with vector b? I'm puzzled as to how to do that, and as it happens, I'm meant to solve a set of questions using the same method later on in my assignment.



If you want to use the suggested method, start by dotting with b. Rearrange to get an expression for (x.b). You can then substitute this expression back into the original equation, and the answer drops out.
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MFAHH
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Aha! Thanks a lot davros and ClickItBack, I've finally got the answer! Much appreciated :biggrin:. Any ideas on a strategy to tackle the next question?
Reply 7
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MFAHH
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Any one got an idea how I could proceed with the vector diagram question? Here's the little I've done so far:

20140203_163638.jpg

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