Question

Let P, Q, R and S be the points on the plane with position vectors
$-2\hat{i}-\hat{j},4\hat{i},3\hat{i}+3\hat{j}and-3\hat{i}+2\hat{j}$, respectively. The quadrilateral PQRS must be a

• A. parallelogram, which is neither a rhombus nor a rectangle
• B. square
• C. rectangle, but not a square
• D. rhombus, but not a square

Answer 1

The correct option is A

parallelogram, which is neither a rhombus nor a rectangle

$m_{PQ}=\frac{1}{6},m_{SR}=\frac{1}{6},m_{RQ}=-3,m_{SP}=-3$

$\Rightarrow$ Parallelogram, but neither $PR=SQ$ nor $PR\perp SQ$
$\therefore$ So, it is a parallelogram, which is neither a rhombus nor a rectangle.