If the plane 2ax−3ay+4az+6=0 passes through the mid-point of the line joining the centres of the spheres x2+y2+z2+6x−8y−2z=13 and x2+y2+z2−10x+4y−2z=8, then a equals
Solutions · 1
Official solution
Centers of given spheres are \[\left( { - 3,4,1} \right)\] and \[\left( {5, - 2,1} \right).\]
Mid point of centers is \[\left( {1,1,1} \right).\]
Satisfying this in the equation of plane, we get
2a−3a+4a+6=0
\[ \Rightarrow a = - 2\]