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P3 Vectors.... watch

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    FInd a vector which is perpendicular to both a and b where:

    e) a = 2i - 3j - 4k, b = 4i -3j + k

    CHeers.
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    5i + 6j - 2k.
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    (Original post by jonnymcc2003)
    FInd a vector which is perpendicular to both a and b where:

    e) a = 2i - 3j - 4k, b = 4i -3j + k

    CHeers.
    It looks impossible - two equations and three unknowns

    MB
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    No the guy above got it right.

    The method would be nice however...
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    Sorry, I used the cross product and did the working in my head. However, if you would like a passable P3-style solution:

    Let the vector you want be xi + yj + zk.

    If you dot this vector with your two given vectors, you get 0

    => 2x - 3y - 4z = 0
    and 4x - 3y + z = 0

    Like musicboy said, there are two equations and three unknowns, so you cannot obtain a unique solution of x, y and z. However, all the possible values of x, y and z will be scalar multiples of each other, so it doesn't matter.

    Equate your two equations to give:

    -2x = 5z

    Therefore 1.2x = y

    Stick in any value of x (say 1)

    Thus your vector is 1i + 1.2j - 0.4k

    or multiply it thrhough by 5 to get integer coefficients of i, j and k.

    and your answer is 5i + 6j - 2k as required.
 
 
 
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