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JEE Main2012MathematicsThree Dimensional GeometryActual

If the three planes x=5,2 x-5 a y+3 z-2=0 and 3 b x+y-3 z=0 contain a common line, then (a, b) is equal to

Options

  1. A( 8 15 ,- 1 5 )
  2. B( 1 5 ,- 8 15 )
  3. C(- 8 15 , 1 5 )
  4. D(- 1 5 , 8 15 )

Correct answer

B. ( 1 5 ,- 8 15 )

Step-by-step solution

Let the direction ratios of the common line be , m and n . aligned & 1+ m 0+ n 0=0 =0 & 2 -5 m a+3 n=0 5 m a-3 n=0 & 3 b+m-3 n=0 m-3 n=0 aligned Subtracting (3) from (1), we get m(5 a-1)=0 Now, value of m can not be zero because if m=0 then n=0 =m=n=0 which is not possible. Hence, 5 a-1=0 a= 1 5

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