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JEE Advanced2007MathematicsThree Dimensional GeometryActual

Consider the planes 3 x-6 y-2 z=15 and 2 x+y-2 z=5 . Statement I The parametric equations of the line of intersection of the given planes are x=3+14 t, y=1+2 t and z=15 t . Statement II The vectors 14 i +2 j +15 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 3 x-6 y-2 z=15 and 2 x+y-2 z=5 For z=0 , we get x=3, y=-1 Direction ratios of planes are and then the dr's of line of intersection of planes is 14215 and line is aligned x-3 14 & = y+1 2 = z-0 15 = (say) x & =14 +3, y=2 -1, z=15 aligned Hence, Statement I is false. But Statement II is true.

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