Vectors 1 Question 8

9. 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 $P Q R S$ must be a

(2010)

(a) parallelogram, which is neither a rhombus nor a rectangle

(b) square

(c) rectangle, but not a square

(d) rhombus, but not a square

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Answer:

Correct Answer: 9. (a)

Solution:

  1. $m _{P Q}=\frac{1}{6}, m _{S R}=\frac{1}{6}, m _{R Q}=-3, m _{S P}=-3$

$\Rightarrow$ Parallelogram, but neither $P R=S Q$ nor $P R \perp S Q$.

$\therefore$ So, it is a parallelogram, which is neither a rhombus nor a rectangle.



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