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

  • Option 1)

    1

  • Option 2)

    –1

  • Option 3)

    2

  • Option 4)

    –2

 

Answers (1)

As we learnt in

General equation (cartesian form ) -

ax+by+cz+d= 0

-

 

 Centre of S_{1}:C_{1}\left ( -3,4,1 \right )

Centre of S_{2}:C_{2}\left ( 5,-2,1 \right )

Midpoint of  C_{1}C_{2}\, \, \, is\, \, \left ( 1,1,1 \right )

2ax-3ay+4az+6=0 passes through (1,1,1)

2a-3a+4a+6=0

a=-2


Option 1)

1

Incorrect Option

 

Option 2)

–1

Incorrect Option

 

Option 3)

2

Incorrect Option

 

Option 4)

–2

Correct Option

 

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