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The plane 6 x+k y+3 z-12=0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x^2+y^2+z^2-2 x-3 y-4 z=0 . If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correct?

Options

  1. A0 p 0.5
  2. B0.5 p 1
  3. C1 p 1.5
  4. Dp 1.5

Correct answer

B. 0.5 p 1

Step-by-step solution

Perpendicular distance from centre (1, 3 2 , 2 ) to theplane aligned & 6 x+4 y+3 z-12=0 & P= 6+4 ( 3 2 )+3(2)-12 36+16+9 & = 6+6+6-12 61 = 6 61 =0.74 aligned

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