PQRS is a parallelogram. If $straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top$ are the position vectors of the vertices P, Q and R respectively with reference to the origin of reference O ; find the position vector of S with reference to O.

We have $QP with rightwards arrow on top space equals space straight P. straight V. space of space straight P space minus space straight P. straight V. space of space straight Q space equals space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top$
$But space RS with rightwards arrow on top space equals space QP with rightwards arrow on top space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space space PQRS space is space straight a space vertical line vertical line space gm close square brackets$
$therefore space space space space space space space space space space space space RS with rightwards arrow on top space equals space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top$
Now position vector of S with reference to O = $OS with rightwards arrow on top$
$equals space OR with rightwards arrow on top space plus space RS with rightwards arrow on top space equals space straight c with rightwards arrow on top space plus space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top$

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PQRS is a parallelogram. If are the position vectors of the vertices P, Q and R respectively with reference to the origin of reference O ; find the position vector of S with reference to O.

Vector Algebra

Mathematics Part II