EAMCET Engineering 2010 Solved Paper

The equation of the sphere is
x2+y2+z2−6x−12y−2z+20=0So, the centre of the sphere is
(−u,−v,−w)=(3,6,1)
given the one end of the diameter is ( 2,3,−3), let the other end of the diameter is (α,β,γ).
Since, O is the mid point of the diameter, then
‌(3,6,1)=[‌

α+2

2

,‌

β+3

2

,‌

γ−3

2

]
‌⇒‌‌‌

α+2

2

=3,α=4
‌⇒‌‌‌

β+3

2

=6,β=9
‌⇒‌‌‌

γ−3

2

=1,γ=5
Hence, the other end is (4,9,5).