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Thread: 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

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

    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?
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