A) (4, 9,-3)
B) (4,-3, 3)
C) (4, 3, 5)
D) (4, 3, -3)
Correct Answer: A
Solution :
Equation of sphere is \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2z+20=0\] Whose coordinates of centre are (3, 6, 1). Let the coordinates of the other end of diameter be \[(\alpha ,\beta ,\gamma )\] then \[\frac{\alpha +2}{2}=3,\frac{\beta +3}{2}=6,\frac{\gamma +5}{2}=1\] Hence,\[\alpha \,\text{= }4,\text{ }\beta =9\]and \[\gamma =-3\]. Thus, the coordinates of other point are (4, 9, - 3).
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