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