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Math Help - parallelogram using vectors

  1. #1
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    Exclamation parallelogram using vectors

    given the four points:
    A= (1,4,-2) B=(5,6,-2) C=(3,0,2) D=(7,2,2)

    show that ABCD is a parallelogram using vectors.
    is it a parallelogram? square? rhombus?





    if I'm correct, in order for vectors to be parallel, they must be scalar multiples of one another. So i found the vectors of these points, but I got

    vector AB= <4,2,-4>
    vector BC=<-2,-6,4>
    vector CD= <4,2,0>
    vector AD= <-6,2,4>


    not sure what I did wrong
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  2. #2
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    Quote Originally Posted by cottekr View Post
    given the four points:
    A= (1,4,-2) B=(5,6,-2) C=(3,0,2) D=(7,2,2)

    show that ABCD is a parallelogram using vectors.
    is it a parallelogram? square? rhombus?





    if I'm correct, in order for vectors to be parallel, they must be scalar multiples of one another. So i found the vectors of these points, but I got

    vector AB= <4,2,-4> <4,2,0>
    vector BC=<-2,-6,4>
    vector CD= <4,2,0>
    vector AD= <-6,2,4> <6,-2,4>
    only two sides parallel ... sure you have the correct coordinates?
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  3. #3
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    \begin{array}{l}<br />
 \overrightarrow {AB}  = \left\langle {4,2,0} \right\rangle  \\ <br />
 \overrightarrow {BC}  = \left\langle { - 2, - 6,4} \right\rangle  \\ <br />
 \overrightarrow {CD}  = \left\langle {4,2,0} \right\rangle  \\ <br />
 \overrightarrow {DA}  = \left\langle { - 6,2, - 4} \right\rangle  \\ <br />
 \end{array}
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