The shortest distance from \( (1,1,1) \) to the line of intersection of the pair of plane \( x y...

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The shortest distance from \( (1,1,1) \) to the line of intersection of the pair of plane \( x y+y z+z x+y^{2}=0 \)
(a) \( \sqrt{\frac{8}{3}} \)
(b) \( \frac{2}{\sqrt{3}} \)
(c) \( \frac{1}{\sqrt{3}} \)
(d) \( \frac{2}{3} \)
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