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Math Help - vectors

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    MHF Contributor ebaines's Avatar
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    Re: vectors

    Do you know how to add vectors? Break them into x- and y-components and add the components, then convert back to magnitude and direction. So - what are the x- and y- components of vectors a, b, and c? What do get for the sum of all three vectors? Finally - what is the magnitude of ths sum of all three vectors?
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    Re: vectors

    That's probably the simplest thing to do. But you could also use the "cosine law".
    It should be clear that \vec{a}+ \vec{c} has length 10- 2= 8 and is in the direction of c.

    Now, adding \vec{b} to that, we have a triangle with sides of length 8 and 3 and angle 180- 120= 60 between them. The length, x, of the third side of that triangle satisifies x^2= 3^2+ 8^2- 2(3)(8)cos(60)= 9+ 64- 48(1/2)= 49 so x= 7. The angle, A, that side makes with \vec{a} is given by the sin law: \frac{sin(A)}{3}= \frac{sin(60)}{7}.
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    Re: vectors

    10 - 2 - 3cos(60) = 8 - 3cos(60)

    = 8 - 3/2

    = 13/2

    The vertical components are

    0 + 0 + 3sin(60) = 3sin(60

    = (3/2) sqrt(2)
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