A) \[(-3,-4,-5)\]
B) \[(3,4,5)\]
C) \[(3,4,-5)\]
D) \[(-3,4,-5)\]
Correct Answer: B
Solution :
[b] The equation of the given sphere is \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10z=0.\] \[\therefore \] Its centre is (0, 0, 5). Coordinates of one end point of a diameter of the sphere is given as (-3, -4, 5). Let coordinates of another end point of this diameter \[({{x}_{1}},{{y}_{1}},{{z}_{1}})\] \[\therefore \frac{-3+{{x}_{1}}}{2}=0\Rightarrow {{x}_{1}}=3\] \[\frac{-4+{{y}_{1}}}{2}=0\Rightarrow {{y}_{1}}=4\] and \[\frac{5+{{z}_{1}}}{2}=5\,\,\,\,\,\,\,\Rightarrow {{z}_{1}}=5\] \[\therefore \] Required coordinates are (3, 4, 5).
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