Vectors and Magnitudes

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Feb 15th 2009, 01:29 PM
92stealth

Vectors and Magnitudes

Find the component form of a vector v given the magnitude of u and u+v and the angles that u and u+v make with the positive x-axis.

sorry, fixed.....
||u||=2, $\theta$ = 230, ||u+v|| = 8 $\theta$ = 80

I can't find any problem like this in the book, instructor gave us this as a take home problem to work on.... (Thinking)
Feb 15th 2009, 01:36 PM
Legendsn3verdie

red x bro.. can't see anything..
Feb 15th 2009, 01:40 PM
Reckoner

Quote:

Originally Posted by 92stealth

Find the component form of a vector v given the magnitude of u and u+v and the angles that u and u+v make with the positive x-axis.

If you have the magnitude of $\textbf u$ and $\textbf u+\textbf v,$ along with their angles, it should be easy to get their component forms. Once you have that, $\textbf v$ is simply $\textbf (\textbf u+\textbf v)-\textbf u\text.$

You could also set it up as a triangle with sides of length $\lVert\textbf u\rVert, \lVert\textbf v\rVert,$ and $\lVert\textbf u+\textbf v\rVert,$ and angle $|\theta_1-\theta_0|.$ You can use the law of cosines to get $\lVert\textbf v\rVert\text.$

Edit: Now that you have posted the actual values, I see that your problem is much simpler. $\textbf u$ and $\textbf u+\textbf v,$ make the same angle with the $x$ -axis, which means that they are parallel. What does that tell you about $\textbf v?$
Feb 15th 2009, 01:52 PM
92stealth

wow, i am 100% not on my game today. I messed up that first post once again, should have been 80 degrees on the second -.- sorry