A) (1, 0, 10)
B) (1, 0, -10)
C) (-1, 0, 10)
D) None of these
Correct Answer: B
Solution :
The equation of the sphere is \[\left| r-2\vec{i}-\vec{j}+6\vec{k} \right|=\sqrt{18}\] \[\Rightarrow \]Its centre is at the point\[(\vec{r}-2\vec{i}-\vec{j}+6\vec{k})\], i.e, at \[(2,1,-6).\] coordinates of A are\[(3,2,-2)\]. Let the coordinates of B be\[(\alpha ,\beta ,\gamma )\]. Then, \[\frac{3+\alpha }{2}=2,\frac{2+\beta }{2}=1\] and \[\frac{-2+\lambda }{2}=-6\] \[\Rightarrow \alpha =1,\beta =0,\lambda =-10\] Therefore, coordinates of B are \[(1,0,-10).\]
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