Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2007Paper 2
Exam
JEE Advanced
Year
2007
Paper
Paper 2
Subject
Mathematics
Chapter
Three Dimensional Geometry

JEE Advanced 2007 · Paper 2 · Mathematics · Three Dimensional Geometry

Consider the planes 3 x-6 y-2 z=15 and 2 x+y-2 z=5 . Statement I...

Consider the planes 3x−6y−2z=153 x-6 y-2 z=15 and 2x+y−2z=52 x+y-2 z=5. Statement I The parametric equations of the line of intersection of the given planes are x=3+14t,y=1+2tx=3+14 t, y=1+2 t and z=15tz=15 t. Statement II The vectors 14i^+2j^+15k^14 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+15 \hat{\mathbf{k}} is parallel to the line of intersection of the given planes.

Options

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

Correct answer

D. Statement I is false, Statement II is true

Step-by-step solution

Given planes are 3x−6y−2z=15and2x+y−2z=53 x-6 y-2 z=15 and 2 x+y-2 z=5 For z=0z=0, we get x=3,y=−1x=3, y=-1 Direction ratios of planes are < 3-6-2> and \text{ and }< 2 \quad 1-2> then the dr′soflineofintersectionofplanesis⟨14215⟩andlineisdr's of line of intersection of planes is\langle 14215\rangle and line isx−314=y+12=z−015=λ (say) ⇒x=14λ+3,y=2λ−1,z=15λ\begin{aligned}\frac{x-3}{14}& =\frac{y+1}{2}=\frac{z-0}{15}=\lambda \text{ (say) }\\ \Rightarrow \quad x & =14 \lambda+3, y=2 \lambda-1, z=15 \lambda \end{aligned}$Hence, Statement I is false. But Statement II is true.
Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Let P be the plane such that it contains the straight line (x-1)/(2) = (y-3)/(3) =… JEE Advanced 2026Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1) . Let S be the… JEE Advanced 2026Let the foot of perpendicular from the point (λ, 2, 3) on the line (x-4)/(1) = (y-9)/(2)… JEE Main 2026Let a line L_1 pass through the origin and be perpendicular to the lines L_2: r = (3+t) i… JEE Main 2026The shortest distance between the lines (x-4)/(1) = (y-3)/(2) = (z-2)/(-3) and (x+2)/(2)… JEE Main 2026Let the image of the point P(0, -5, 0) in the line (x-1)/(2) = (y)/(1) = (z+1)/(-2) be… JEE Main 2026Let the image of the point P(1, 6, a) in the line L: (x)/(1) = (y-1)/(2) = (z-a+1)/(b)… JEE Main 2026Let a line L be perpendicular to both the lines L_1: (x+1)/(3) = (y+3)/(5) = (z+5)/(7)… JEE Main 2026Let a triangle PQR be such that P and Q lie on the line (x+3)/(8) = (y-4)/(2) = (z+1)/(2)… JEE Main 2026If the distance of the point (a, 2, 5) from the image of the point (1, 2, 7) in the line… JEE Main 2026The square of the distance of the point P(5, 6, 7) from the line (x-2)/(2) = (y-5)/(3) =… JEE Main 2026The square of the distance of the point of intersection of the lines r = ( i + j - k ) +… JEE Main 2026The shortest distance between the lines r =((1)/(3) i +2 j +(8)/(3) k )+λ(2 i -5 j +6 k )… JEE Main 2026If (2α+1, α^2-3α, (α-1)/(2)) is the image of (α, 2α, 1) in the line… JEE Main 2026A line with direction ratios 1, -1, 2 intersects the lines (x)/(2) = (y)/(3) = (z+1)/(3)… JEE Main 2026The square of the distance of the point (-2, -8, 6) from the line (x-1)/(1) = (y-1)/(2) =… JEE Main 2026 Full Three Dimensional Geometry list Three Dimensional Geometry JEE Maths PYQsJEE Mathematics PYQs All JEE Advanced PYQs