IIT-JEE 2010 · Paper 1 · Mathematics Q32

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MathematicsSingle correct+3 / -1Question 32 of 84

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

parallelogram, which is neither a rhombus nor a rectangle

square

rectangle, but not a square

rhombus, but not a square

Answer and worked solution

Official answer: A

Sides. $\overrightarrow{PQ}=(6,1)$ , $\overrightarrow{SR}=(6,1)$ : equal, so PQRS is a parallelogram. $\overrightarrow{QR}=(-1,3)$ .

Rectangle? $\overrightarrow{PQ}\cdot\overrightarrow{QR}=-6+3=-3\ne0$ . No.

Rhombus? $|PQ|=\sqrt{37}$ , $|QR|=\sqrt{10}$ . No.

(A)

Topics:Vector operations Dot product

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IIT-JEE 2010 · Paper 1, Mathematics question 32