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Attachment 19601

I'm having some troubles defining vector OA in both images. Does anyone know how?

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- Nov 6th 2010, 12:08 PMAniMuSDefining a vector
Attachment 19600

Attachment 19601

I'm having some troubles defining vector OA in both images. Does anyone know how? - Nov 6th 2010, 01:19 PMAckbeet
In the first picture, you have

$\displaystyle |OB|=|BA|=b.$

Hence, $\displaystyle OAB$ is isosceles. Therefore, $\displaystyle \angle OAB=\angle AOB=\theta.$

Therefore, $\displaystyle \angle ABO=\pi-2\theta.$

Now we use the law of sines to find $\displaystyle |OA|.$ That is,

$\displaystyle \dfrac{\sin(\theta)}{b}=\dfrac{\sin(\pi-2\theta)}{|OA|}.$

Solve for $\displaystyle |OA|.$

Finally, you can use the expression

$\displaystyle OA=|OA|\langle\sin(\theta),\cos(\theta)\rangle$ to find the final vector $\displaystyle OA.$

In the second problem, you just have the usual

$\displaystyle OA=r\langle\cos(\theta),\sin(\theta)\rangle$. Or do you need to express the vectors using different variables?