The equation |r|^2 - r cdot (2i + 4j - 2k) - | vedclass

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(C) The general equation of a sphere in vector form is given by $|r|^2 - 2(r \cdot a) + c = 0$,where the radius is $\sqrt{|a|^2 - c}$.Comparing the gi

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Sphere of radius $4$

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(C) The general equation of a sphere in vector form is given by $|r|^2 - 2(r \cdot a) + c = 0$,where the radius is $\sqrt{|a|^2 - c}$.Comparing the given equation $|r|^2 - r \cdot (2i + 4j - 2k) - 10 = 0$ with the standard form:Here,$2a = (2i + 4j - 2k)$,which implies $a = (i + 2j - k)$.Also,$c = -10$.The radius of the sphere is $\sqrt{|a|^2 - c}$.Calculating $|a|^2 = |i + 2j - k|^2 = 1^2 + 2^2 + (-1)^2 = 1 + 4 + 1 = 6$.Substituting the values,the radius is $\sqrt{6 - (-10)} = \sqrt{6 + 10} = \sqrt{16} = 4$.Thus,the equation represents a sphere of radius $4$.

The equation $|r|^2 - r \cdot (2i + 4j - 2k) - 10 = 0$ represents a

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