AP EAMCET · Maths · Vector Algebra
If the points \(\mathbf{P}=\hat{i}+2 \hat{j}, \mathbf{Q}=4 \hat{i}+6 \hat{j}\), \(\mathbf{R}=5 \hat{i}+7 \hat{j}, \mathbf{S}=a \hat{i}+b \hat{j}\) are the consecutive vertices of a parallelogram \(P Q R S\), then
- A \(a=2, b=4\)
- B \(a=3, b=4\)
- C \(a=2, b=3\)
- D \(a=3, b=5\)
Answer & Solution
Correct Answer
(C) \(a=2, b=3\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} & \mathbf{P}=\hat{i}+2 \hat{j} \\ & \mathbf{Q}=4 \hat{i}+6 \hat{j} \\ & \mathbf{R}=5 \hat{i}+7 \hat{j} \\ & \mathbf{S}=a \hat{i}+b \hat{j}\end{aligned}\) Let \(A\) be the point of intersection of diagonals \(P R\) and \(Q S\). \(\Rightarrow A\) is the…
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