AIEEE 2005 (Offline)Question 1
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 :
3D Geometry
Solution
Centres $(-3,4,1)$ and $(5,-2,1)$, midpoint $(1,1,1)$: $2a-3a+4a+6=0\Rightarrow a=-2$.