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JEE Advanced 2008Paper 1
Exam
JEE Advanced
Year
2008
Paper
Paper 1
Subject
Mathematics
Chapter
Determinants

JEE Advanced 2008 · Paper 1 · Mathematics · Determinants

Consider three planes P_1: x-y+z=1, P_2: x+y-z=-1 and P_3: x-3 y+3...

Consider three planes P_1: x-y+z=1, P_2: x+y-z=-1 and P3:x−3y+3z=2P_3: x-3 y+3 z=2 Let L1,L2L_1, L_2 and L3L_3 be the lines of intersection of the planes P2P_2 and P3,P3P_3, P_3 and P1,P1P_1, P_1 and P2P_2, respectively. Statement 1 Atleast two of the lines L1,L2L_1, L_2 and L3L_3 are non-parallel. Statement 2 The three planes do not have a common point.Consider three planes P_1: x-y+z=1, P_2: x+y-z=-1 and P_3: x-3 y+3 z=2 Let L_1, L_2 and L_3 be the lines ofConsider three planes P_1: x-y+z=1, P_2: x+y-z=-1 and P_3: x-3 y+3 z=2 Let L_1, L_2 and L_3 be the lines of

Options

  1. AStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  2. BStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  3. CStatement 1 is true, Statement 2 is false.
  4. DStatement 1 is false, Statement 2 is true

Correct answer

D. Statement 1 is false, Statement 2 is true

Step-by-step solution

The given equations are x−y+z=1,x+y−z=−1 and x−3y+3z=2\begin{aligned}& x-y+z=1, \\ & x+y-z=-1 \text{ and }x-3 y+3 z=2 \end{aligned}The system of equations can be put in matrix form asAX=B<imgsrc="/api/proxy−image?url=httpsA X=B<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_advanced%252FZ98dskolD9r3E84JgOJxxxWAm-WJoBebFfGiKjaOBfQ.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FZ98dskolD9r3E84JgOJxxxWAm-WJoBebFfGiKjaOBfQ.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FZ98dskolD9r3E84JgOJxxxWAm-WJoBebFfGiKjaOBfQ.original.fullsize.png?alt=media"> \\ which is inconsistent as ρ(A:B)≠ρ(A)\rho(A: B) \neq \rho(A). \RightarrowTheThethree planes do not have a common point. \Rightarrow Statement 2 is true. Since, planesP1,P2andP3P_1, P_2 and P_3 are pairwise intersection, their lines of intersection are parallel. Statement 1 is false.
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