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Math Help - Parallelogram Question

  1. #1
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    Parallelogram Question

    ABC has vertices of A(3,2,-5) B(4,-1,7) C(-8,3,-6)

    Determine the coordinates of D such that ABCD is a parallelogram

    Is the parallelogram a rectangle? Justify your answer.
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  2. #2
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    Hello,
    Quote Originally Posted by peon123 View Post
    ABC has vertices of A(3,2,-5) B(4,-1,7) C(-8,3,-6)

    Determine the coordinates of D such that ABCD is a parallelogram

    Is the parallelogram a rectangle? Justify your answer.
    \vec{AB}=\vec{DC}

    that should give you the coordinates of D.

    As to know whether it's a rectangle or not... you should know that a rectangle is a parallelogram with a right angle.
    So check if the scalar product between \vec{AB} and \vec{BC} is 0.


    Memo : x_a,y_a,z_a) \text{ and } Bx_b,y_b,z_d) \quad \Rightarrow \quad \vec{AB}x_b-x_a,y_b-y_a,z_b-z_a)" alt="Ax_a,y_a,z_a) \text{ and } Bx_b,y_b,z_d) \quad \Rightarrow \quad \vec{AB}x_b-x_a,y_b-y_a,z_b-z_a)" />
    (coordinates of vector)
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