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April 20, 2014

April 20, 2014

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

- CALCULUS -
**Damon**, Sunday, May 23, 2010 at 6:47pmvector 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 -
**drwls**, Sunday, May 23, 2010 at 6:56pmYour 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 -
**Damon**, Sunday, May 23, 2010 at 7:02pmLOL , if opposite sides with four sides are parallel, it is a parallelogram.

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