Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}…
Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, 4 \hat{\mathbf{i}}, 3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ and $-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ respectively. The quadrilateral $P Q R S$ must be a
parallelogram, which is neither a rhombus nor a rectangle
square
rectangle, but not a square
rhombus, but not a square
Solution
$m_{P Q}=\frac{1}{6}, m_{S R}=\frac{1}{6}, \quad m_{R Q}=-3$, $m_{S P}=-3$
$\Rightarrow$ Parallelogram
But neither $P R=S Q$ nor $P R \perp S Q$.
$\therefore$ Parallelogram, which is neither a rhombus nor a rectangle.
