Vector Proof: Given OP = -2i + 2j, OQ = -2j, OR = 5i + 3j

[seek_solutions]

Given OP = -2i + 2j, OQ = -2j, OR = 5i + 3j, OS = 3i + 7j, prove PQRS is a parallelogram.

WHat i did was work out PQ = 2i - 4j and RS = -2i + 4j

and QR = 5i + 5j and SP = -5i - 5j

But I am stuck now!

 

[pka]

All you need is to see that oppsite sides are parallel and have the same length:
\(\displaystyle \L
\vec {PQ} = - \vec{RS} \quad \& \quad \left\| {\vec{PQ} } \right\| = \left\| {\vec{RS} } \right\|\)

 

[seek_solutions]

Hi pka thanks for that! Why is your name pka? I'm just curious.