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Math Help - Problem

  1. #1
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    Problem

    Demonstrate , using the definition of the dot product, that the length of the vectors a and b are equal if an only if the diagonals of the quadrilateral OAQB are orthogonal.

    A Q




    O B

    its meant to be a rhombus


    Hint: Use that if (OA-OB) is perependicualr to (OA+OB) then OA = OB and vice versa.

    P.S dont tell me the answer just need some help of what to do help much appreciated
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  2. #2
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    please help i need to do this a.s.a.p
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  3. #3
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    Quote Originally Posted by adam_leeds View Post
    Demonstrate , using the definition of the dot product, that the length of the vectors a and b are equal if an only if the diagonals of the quadrilateral OAQB are orthogonal.
    Take O as the origin, A as the point with position vector a, B as the point with position vector b. Then Q has position vector a + b. The vector from B to A is a - b, and the condition for these two vectors to be perpendicular is (a + b).(a - b) = 0.
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  4. #4
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    Quote Originally Posted by Opalg View Post
    Take O as the origin, A as the point with position vector a, B as the point with position vector b. Then Q has position vector a + b. The vector from B to A is a - b, and the condition for these two vectors to be perpendicular is (a + b).(a - b) = 0.
    thanks for the help
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