Let P, Q, R and S be the points on the plane with position vectors `-2hati-hatj,4hati,3hati+3hatj and -3hati+2hatj` respectively. The quadrilateral PQRS must be a

Options

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

Answer

A

Explanation

Now , `PQ=6hat(i)+hat(j)`
`QR=-hat(i)+3hat(j)`
`RS=-6hat(i)-hat(j)`
`SP=hat(i)-3hat(j)`
`rArr |PQ|=sqrt(37)=|RS|`
`|QR|=sqrt(10)=|SP|`
`therefore PQ.QR=-6+3=-3 ne 0` .