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Thread: quick vector problem

  1. #1
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    quick vector problem

    Determine ||v+w|| if v and w are unit vectors separated by 0.3 radians
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    First thing to do is draw a diagram of the triangle. Two sides are 1 and the angle between them is $\displaystyle \pi-0.7$. Use cosine rule to find the distance required.
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  3. #3
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    Quote Originally Posted by casesam View Post
    Determine ||v+w|| if v and w are unit vectors separated by 0.3 radians
    Let $\displaystyle \vec w = (1, 0)$

    Since $\displaystyle |\vec w| = |\vec v|$ you can express $\displaystyle \vec v$ as:

    $\displaystyle \vec v = |\vec w|(\cos(0.3), \sin(0.3))$

    Therefore

    $\displaystyle \vec v + \vec w = |\vec w|(1+\cos(0.3), \sin(0.3))$

    Now calculate

    $\displaystyle |\vec v + \vec w| = |\vec w|\sqrt{(1+\cos(0.3))^2+(\sin(0.3))^2}\approx 1.9778$ because $\displaystyle |\vec w| = 1$.
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