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The radius of the sphere 2(x2 + y2 + z2) - 2x + 4y - 6z = 15 is
1. \(\frac{\sqrt{11}}{2}\) units
2. √11 units
3. \(\sqrt{\frac{11}{2}}\) units
4. None of the above

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Correct Answer - Option 2 : √11 units

Concept:

Equation of sphere in standard form: 

\(x^{2}+y^{2}+z^{2}+2u x+2 v y+2 w z+d=0\)

The radius of the sphere:

 \(r=\sqrt{u^{2}+v^{2}+w^{2}-d}\)

Calculation:

Given: 2(x2 + y2 + z2) - 2x + 4y - 6z = 15 

Divide by 2, we get,

x2 + y2 + z2 – x + 2y - 3z - \(\frac{15}{2}\) = 0

Comparing above equation with the standard equation of sphere, we get 

2u = -1 ⇒ u = -1/2,

2v = 2 ⇒ v = 1,

2w = -3 ⇒ w = -3/2

d = -\(\frac{15}{2}\)

Now, Radius of sphere

  \(r=\sqrt{u^{2}+v^{2}+w^{2}-d}\)

⇒ r = \(\sqrt{(\frac{-1}{2})^2+1^2+(\frac{-3}{2})^2 - (\frac{-15}{2})}\)

⇒ r = \(\sqrt{\frac{1}{4}+1+\frac{9}{4}+ (\frac{15}{2})}\)

⇒ r = √11 

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