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March 30, 2017

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Given vectors A = -4.8i + 6.8j and B = 9.6i + 6.7j, determine the vector C that lies in the xy plane perpendicular to B and whose dot product with A is 20.0.

  • Vectors - ,

    let the vector C = [a,b]

    then using the dot product condition:
    -4.8a + 6.8b = 20
    or
    12a - 17b = -50

    slope of vector B is 6.7/9.6 or 67/96
    slope of vector C is b/a
    since the are perpendicualr
    b/a = - 96/67
    b = -96a/67
    subbing back into first equation,
    12a - 17(-96a/67) = -50
    solving this I got
    a = -1675/1218
    and then back into the first ...
    b = 400/203

    so vector C = [-1675/1218, 400/203]

    I will leave it up to you to check it out, it does work.

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