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If the plane 2 a x-3 a y+4 a z+6=0 passes through the midpoint of the line joining the centres of the spheres x^2+y^2+z^2+6 x-8 y-2 z=13 and x^2+y^2+z^2-10 x+4 y-2 z=8 , then a equals

Options

  1. A-1
  2. B1
  3. C-2
  4. D2

Correct answer

C. -2

Step-by-step solution

Plane 2 a x-3 a y+4 a z+6=0 passes through the mid point of the centre of spheres x^2+y^2+z^2+6 x-8 y-2 z=13 and x^2+y^2+z^2-10 x+4 y-2 z=8 respectively centre of spheres are (-3,4,1) &(5,-2,1) Mid point of centre is (1,1,1) Satisfying this in the equation of plane, we get 2 a-3 a+4 a+6=0 a=-2

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