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JEE Advanced 2010Paper 1
Exam
JEE Advanced
Year
2010
Paper
Paper 1
Subject
Mathematics
Chapter
Vector Algebra

JEE Advanced 2010 · Paper 1 · Mathematics · Vector Algebra

Let P, Q, R and S be the points on the plane with position vectors...

Let P,Q,RP, Q, R and SS be the points on the plane with position vectors −2i^−j^,4i^,3i^+3j^-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, 4 \hat{\mathbf{i}}, 3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}} an d−3i^+2j^\mathrm{d}-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}} respectively. The quadrilateral PQRSP Q R S must be aLet P, Q, R and S be the points on the plane with position vectors -2 i - j , 4 i , 3 i +3 j an d-3 i +2 j

Options

  1. Aparallelogram, which is neither a rhombus nor a rectangle
  2. Bsquare
  3. Crectangle, but not a square
  4. Drhombus, but not a square

Correct answer

A. parallelogram, which is neither a rhombus nor a rectangle

Step-by-step solution

mPQ=16,mSR=16,mRQ=−3m_{P Q}=\frac{1}{6}, m_{S R}=\frac{1}{6}, \quad m_{R Q}=-3, mSP=−3m_{S P}=-3 Let P, Q, R and S be the points on the plane with position vectors -2 i - j , 4 i , 3 i +3 j an d-3 i +2 j
⇒\Rightarrow Parallelogram But neither PR=SQP R=S Q nor PR⊥SQP R \perp S Q. ∴\therefore Parallelogram, which is neither a rhombus nor a rectangle.
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