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Math Help - parallelogram area with 3D vectors

  1. #1
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    parallelogram area with 3D vectors

    How do I find the area of a parallelogram with the given vertices
    K (1, 3, 2) L (1, 4, 4) M (4, 9, 4) N (4, 8, 2)

    I have to use the cross product, but I'm pretty lost.
    Please help!
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  2. #2
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    Quote Originally Posted by acg716 View Post
    How do I find the area of a parallelogram with the given vertices
    K (1, 3, 2) L (1, 4, 4) M (4, 9, 4) N (4, 8, 2)

    I have to use the cross product, but I'm pretty lost.
    Please help!
    For any \vec{u},\vec{v}\in\mathbb{R}^3, \|\vec{u}\times \vec{v}\|=\|\vec{u}\| \|\vec{v}\| |\sin(\vec{u},\vec{v})| equals the area of the parallelogram defined by the points O,O+\vec{u},O+\vec{u}+\vec{v},O+\vec{v}.

    Thanks to the above, the area of KLMN is \|\overrightarrow{KL}\times\overrightarrow{KM}\|: compute the vectors, the cross-product, and then the norm.
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  3. #3
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    what do i do after i find the cross product of KL and KM ??
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  4. #4
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    Quote Originally Posted by acg716 View Post
    what do i do after i find the cross product of KL and KM ??
    Then (like I wrote earlier) the area is given by the norm of this vector: \|(x,y,z)\|=\sqrt{x^2+y^2+z^2}, where (x,y,z) is to be replaced by the cross product.
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