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Math Help - angles and coordinates and vectors

  1. #1
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    angles and coordinates and vectors

    Coordinates of the points A, B and C are (1, 2, 3) , (2, 3, -1) and (3, -1, 1) respectively,

    find vectors ->AB and ->AC

    find the angle <BAC
    to the nearest degree:

    please help with this problem
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  2. #2
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    Quote Originally Posted by rcmango View Post
    Coordinates of the points A, B and C are (1, 2, 3) , (2, 3, -1) and (3, -1, 1) respectively,

    find vectors ->AB and ->AC

    find the angle <BAC
    to the nearest degree:

    please help with this problem
    Well, vector AB will be:
    (2 - 1)i + (3 - 2)j + (-1 - 3)k = i + j - 4k

    Vector AC will be:
    (3 - 1)i + (-1 - 2)j + (1 - 3)k = 2i - 3j - 2k
    (where i, j, and k are the unit vectors in the x, y, and z directions, respectively.)

    We also know that
    (AB) (dot) (AC) = |AB|*|AC|* cos(theta)
    where theta is the angle between the vectors.

    (AB) (dot) (AC) = (1)*(2) + (1)*(-3) + (-4)*(-2) = 7
    |AB| = sqrt{1^2 + 1^2 + 4^2} = sqrt{18} = 3*sqrt{2}
    |AC| = sqrt{2^2 + 3^2 + 2^2} = sqrt{17}

    So cos(theta) = 7/(3*sqrt{2}*sqrt{17})

    Now take the inverse cosine to get the angle.

    -Dan
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