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Math Help - Vector product properties and are of quadrilateral

  1. #1
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    Vector product properties and are of quadrilateral

    "Show, using vector algebra, that the area of a quadrilateral ABCD is given by 1/2|ACBD| where AC and BD are the diagonals of ABCD."

    I understand that in order to answer this question you split the quadrilateral into two triangles and use the formula "area of triangle = 1/2 |a x b|" but I don't understand how you get from the line "A =
    1/2 |ac+cbac|" to "A=1/2 |cb|" in the solutions attached. Surely in order for 'a x c' to be removed it should be '-a x -c' and not just '-a x c'.
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    Re: Vector product properties and are of quadrilateral

    Quote Originally Posted by ehendry91 View Post
    "Show, using vector algebra, that the area of a quadrilateral ABCD is given by 1/2|ACBD| where AC and BD are the diagonals of ABCD."
    I understand that in order to answer this question you split the quadrilateral into two triangles and use the formula "area of triangle = 1/2 |a x b|" but I don't understand how you get from the line "A = 1/2 |ac+cb−ac|" to "A=1/2 |cb|" in the solutions attached. Surely in order for 'a x c' to be removed it should be '-a x -c' and not just '-a x c'.

    Well (a\times c)-(a\times c)=0
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