PQRS is a rhombus. Given that $\overrightarrow{PQ}=a$ and $ \overrightarrow{QR}=b$.

Question

PQRS is a rhombus. Given that $\overrightarrow{PQ}=a$ and $ \overrightarrow{QR}=b$.

(a) express the vectors $\overrightarrow{PR}$ and $ \overrightarrow{QS}$ in terms of $a$ and $b$

(b) hence show that the diagonals in a rhombus intersect at right angles.

My Attempt:

(a) $\overrightarrow{PR}=a+b$ and $\overrightarrow{QS}=b-a $

I have no idea how to work out part (b). Any help is appreciated.

Answer 1

Just take the dot product of diagonals, that is 0( because b=a), hence proved.

Hope it helps.