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
Answer & explanation
Correct answer: option 1
We have,
$\vec{PQ}=\vec{SR}=6\hat i+\hat j$ and $\vec{PS}=\vec{QR}=-\hat i+3\hat j$
Clearly, $\vec{PQ}.\vec{PS}≠0$
Also, $\vec{PR}.\vec{QS}≠0$
Hence, PQRS is a parallelogram but neither a rectangle nor a rhombus.