Given O(0,0),P(1,2),S(-3,0).
P divides OQ in the ratio 2:3 and OPRS is a parallelogram. Find:
i) Coordinate of Q
ii) Coordinate of R
iii) The ratio in which RQ is divided by y axis.
Draw a rough sketch of the situation.
to (i):
$\displaystyle \frac25 \cdot \overrightarrow{OP} = (1,2)$
Calculate the components of $\displaystyle \overrightarrow{OP}$
to (ii):
$\displaystyle \overrightarrow{OP} \parallel \overrightarrow{SR}$
Thus
$\displaystyle \overrightarrow{OR} = \overrightarrow{OS} + \overrightarrow{OP}$
Calculate the components of $\displaystyle \overrightarrow{OR}$
to (iii):
This part is left for you.