Subtracting Vectors - Limited Information

• Mar 20th 2011, 04:53 PM
bdika
Subtracting Vectors - Limited Information
I have no idea how to solve the following problem because there does not seem to be enough information.

Could anyone point me in the right direction?

Here is the problem.

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Suppose vector b has magnitude 8 m/s and direction S24degreesW, the direction of vector b - vector c is east and vector |c| is a minimum. Determine the magnitude and direction of vector c, to one decimal place.

The answer given to this is 7.4 m/s on a bearing of S9degreesE.
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See the diagram below for my understanding of the problem:
Attachment 21207

Any help would be much appreciated.

Thanks.

bdika
• Mar 20th 2011, 06:39 PM
Prove It
For starters, the vector $\displaystyle \displaystyle \mathbf{b} - \mathbf{c}$ in your picture is not pointing east, it's pointing west...
• Mar 21st 2011, 02:38 PM
bdika
Thanks Prove It. I considered the direction wrong but thought that I read somewhere in this forum about the origin of the direction or some such thing. In any case, obviously you are right and thanks for clearing it up for me.

I have some other thoughts on the problem (see image below) but don't know how to proceed. If you haven't already guessed, I am not a mathematician but a Chartered Accountant by profession who studied these things in university more than 30 years ago and now find myself having to relearn them.

Attachment 21219

I'm sorry if I am completely off base. I would appreciate any help that I can get on this.

Thanks.

bdika
• Mar 21st 2011, 05:23 PM
Prove It
First, you need to note that $\displaystyle \displaystyle \mathbf{c} = \mathbf{b} - (\mathbf{b} - \mathbf{c}) = \mathbf{b} + [-(\mathbf{b} - \mathbf{c})]$.

Now that you have your $\displaystyle \displaystyle \mathbf{b} - \mathbf{c}$ pointing in the right direction, you need to reverse its direction, then perform the vector addition, see the following pic...

http://i22.photobucket.com/albums/b3...on/vectors.jpg

Now try to fill in as many missing lengths and angles in your triangle, see where you can go from there...
• Mar 21st 2011, 06:00 PM
skeeter
Quote:
vector c should point the other way, correct?
• Mar 21st 2011, 06:01 PM
Prove It
Quote:

Originally Posted by skeeter
vector c should point the other way, correct?

Yes it should, my apologies...
• Mar 24th 2011, 07:48 AM
bdika
Hi Prove It

However I can't seem to locate the picture that you mentioned in the quote below:

Quote:

Now that you have your pointing in the right direction, you need to reverse its direction, then perform the vector addition, see the following pic...
...or were you referring to my second diagram?

Thanks

bdika
• Mar 24th 2011, 10:06 PM
Prove It
No, it's directly underneath the text... Maybe you should refresh your browser...
• Mar 25th 2011, 06:33 AM
bdika
Thanks Prove It

The picture shows up in my browser at home (Firefox) but not in the browser at work (Internet Explorer). In any case, I have seen the picture and have access to it.

I will work on solving it, and report back my progress.

Thanks.

bdika