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    • Thread Starter

    i have the following question...

    relative to the origin O, A, B, C and D have position vectors

    i + j, i + 1/2j + k, j + k and i + j + k,


    a) calculate the angle between j and the plane ABC

    i have got the following solution:

    AB = (0 , -1/2, 1)

    AC = (0, 1, 1)

    AB x AC = (-1/2, -1, -1/2)

    j = (0, 1, 0)

    (a x b = |a| |b| sin x)

    so j x (AB x AC) = (-1/2, 0, 1/2)

    so (-1/2, 0, 1/2) = 1 * root(3/2) * sinx

    root(2)/2 = root(3/2) * sinx

    sinx = root(1/3)

    however the answers say sinx = root(2/3)?! where have i gone wrong?... im not sure if it is me or the book.. this book has got quite a few errors!!


    you have done it nearly right. The mistake you have made is that you have worked out the angle between j and the normal vector of the plane, when it wanted the angle between j and the plane itself (so all you have to do is add Pi/2 to your angle).

    sinx = root(1/3)
    x = 0.615. . .
    x + Pi/2 = 2.186. . .
    sinx = 0.816 = SQRT[2/3]

    ps: are you the same hikori as on OcUK ?
    • Thread Starter

    yeah its me. alright olly! and yeah that makes sense.. good job u corrected me, my teacher said the book was wrong lol!


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