Let `P ,Q ,R` and `S` be the points on the plane with position vectors `-2i-j , 4i , 3i+3j a n d -3i+2j ,` respectively. The quadrilateral `P Q R S` must be (a) Parallelogram, which is neither a rhombus nor a rectangle (b) Square (c) Rectangle but not a square (d) Rhombus, but not a square

Options

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

a

Explanation

Evaluating midpoint of PR and QS which given
`M=[hati/2+hatj]` same of both.
`vec(OP)= vec(SR)= 6hati +hatj`
` vec(PS)=vec(QR)=-hati+ 3hatj`
`Rightarrow vec(OP).vec(PS) ne 0`
`vec(PQ)||vec(SR),vec(PS)||vec(QR)and |vec(PQ)|=|vec(SR)|,|vec(PS)|=|vec(QR)|`
Hence, PQRS is a parallelgram but not rhombus or rectangle.