SATHEE: Vectors 1 Question 8

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

(d) rhombus, but not a square

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Answer:

Correct Answer: 9. $(\frac{\vec{a} \cdot \vec{b}}{| \vec{b} |^{2}}) \vec{b}$ and $\vec{a} - (\frac{\vec{a} \cdot \vec{b}}{| \vec{b} |^{2}}) \vec{b}$

Solution:

$m_{P Q} = \frac{1}{6}, m_{S R} = \frac{1}{6}, m_{R Q} = - 3, m_{S P} = - 3$

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

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

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Vectors 1 Question 8

9. Let P,Q,R and S be the points on the plane with position vectors −2i^−j^,4i^,3i^+3j^ and −3i^+2j^, respectively. The quadrilateral PQRS must be a

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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