A) \[3\sqrt{3}\]
B) \[\sqrt{3}\]
C) 3
D) \[\frac{1}{3\sqrt{3}}\]
Correct Answer: C
Solution :
[c] Given that. |
\[\left| {{z}_{1}}-i \right|=\left| {{z}_{2}}-i \right|=\left| {{z}_{3}}-i \right|\] |
Hence, \[{{z}_{1}}\],\[{{z}_{2}}\],\[{{z}_{3}}\], lie on the circle whose center is i. |
Also cirucmcenter coincides. |
\[\therefore \frac{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}}{3}=i\] |
\[\Rightarrow \left| {{z}_{1}}+{{z}_{2}}+{{z}_{3}} \right|=3\] |
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