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Math Help - Defining a vector

  1. #1
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    Defining a vector

    Defining a vector-xywh4.jpg
    Defining a vector-fs5q1.jpg

    I'm having some troubles defining vector OA in both images. Does anyone know how?
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  2. #2
    A Plied Mathematician
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    In the first picture, you have

    |OB|=|BA|=b.

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

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

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

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

    Solve for |OA|.

    Finally, you can use the expression

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

    In the second problem, you just have the usual

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