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HELP!! P3 - Quick Question, Exam Tomorrow :( watch

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    ABCD is a parallelogram. The coordinates of A, B and D are (-1,1,2) , (1,2,0) and (1,0,2) respectively.

    Find the coordinates of C.

    ans: (3,1,0) ..apparently B->C = A->D I tried to draw it out but I didn't get it, shouldn't z and y be the same for B+C and A+D if this is true?
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    (Original post by Sugaray)
    ABCD is a parallelogram. The coordinates of A, B and D are (-1,1,2) , (1,2,0) and (1,0,2) respectively.

    Find the coordinates of C.

    ans: (3,1,0) ..apparently B->C = A->D I tried to draw it out but I didn't get it, shouldn't z and y be the same for B+C and A+D if this is true?
    B->C = A-> D

    <=> xBC = xAD and yBC = yAD and zBC = zAD
    <=> xC - xB = xD - xA etc.
    ...

    And finally you get xC=3 and yC=1 and zC=0

    z and y don't have to be the same. A, B, C and D have to be coplanar, but the plan that include them does not necessarily have to be parallel to the plan Oxy.
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    (Original post by zizero)
    B->C = A-> D

    <=> xBC = xAD and yBC = yAD and zBC = zAD
    <=> xC - xB = xD - xA etc.
    ...

    And finally you get xC=3 and yC=1 and zC=0

    z and y don't have to be the same. A, B, C and D have to be coplanar, but the plan that include them does not necessarily have to be parallel to the plan Oxy.
    What does coplanar mean? And how do you get this: B->C = A-> D Thanks
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    (Original post by Sugaray)
    What does coplanar mean? And how do you get this: B->C = A-> D Thanks
    "coplanar" is "in the same plan".

    If ABCD is a # (parallelogram),
    1)AD is parallel to BC. Therefore, A->D = k*B->C with k a real number (ie vector AB is a multiple of vector CD).
    2)d(A,D) = d(B,C). Therefore ¦¦A->D¦¦ = ¦¦B->C¦¦ (the modulus of vector AD equal the modulus of vector BC).

    Therefore, the two vectors are equal.
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    (Original post by zizero)
    "coplanar" is "in the same plan".

    If ABCD is a # (parallelogram),
    1)AD is parallel to BC. Therefore, A->D = k*B->C with k a real number (ie vector AB is a multiple of vector CD).
    2)d(A,D) = d(B,C). Therefore ¦¦A->D¦¦ = ¦¦B->C¦¦ (the modulus of vector AD equal the modulus of vector BC).

    Therefore, the two vectors are equal.
    Ok, thanks But how do you know which is parallel to which? I mean how do you know which corners ABCD are on i.e. they are not just like this

    A------------B


    C------------D

    how do you know it becomes like this?

    A------------D


    B------------C
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    (Original post by Sugaray)
    Ok, thanks But how do you know which is parallel to which? I mean how do you know which corners ABCD are on i.e. they are not just like this

    A------------B


    C------------D

    how do you know it becomes like this?

    A------------D


    B------------C
    When geometrical figures are quoted as a sequence of letters, then you draw them by going from one letter in the sequence to the next letter, "in rotation".
    In your first example,
    A------------B


    C------------D
    you start at A, then go to B, then go to D, then go to C. The order of which is ABDC - not the order given, i.e ABCD!
    Which is why your 2nd example is the correct one.
    A------------D


    B------------C
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    Thank you very much
 
 
 
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