Friday
March 24, 2017

Post a New Question

Posted by on Sunday, May 23, 2010 at 5:44pm.

Show that the quadrilateral with verticies at P(0,2,5), Q(1,6,2), R(7,4,2), and S(6,0,5) is a parallelogram.

  • CALCULUS - , Sunday, May 23, 2010 at 6:47pm

    vector PQ = 1 i + 4 j - 3 k
    vector SR = 1 i + 4 j - 3 k
    parallel

    vector QR = 6 i - 2 j + 0 k
    Vector PS = 6 i - 2 j + 0 k
    parallel
    done

  • CALCULUS - , Sunday, May 23, 2010 at 6:56pm

    Your figure is embedded in three dimensional space, which makes it harder.

    First consider the side lengths:
    PQ: sqrt(1^2 + 4^2 + 3^2) = 5
    QR: sqrt(6^2 + 2^2 + 0) = sqrt40
    RS: sqrt(1^2 + 4^2 + 3^2) = 5
    SP: sqrt(6^2 + 2^2 + 0) = sqrt40
    Next look at the direction cosines. They are the same for the PQ and RS pair, and for the pair QR and SP.

    Opposite sides are of equal length and parallel. Adjacent sides are connected. It must be a parallelogram. There must be a theorem for that.

  • CALCULUS - , Sunday, May 23, 2010 at 7:02pm

    LOL , if opposite sides with four sides are parallel, it is a parallelogram.

Answer This Question

First Name:
School Subject:
Answer:

Related Questions

More Related Questions

Post a New Question