\[ z_{1}=\frac{a}{1-i} ; z_{2}=\frac{b}{2+i} ; z_{3}=a-b i \text { for } a, b \in R \] if \( z_{...

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\[
z_{1}=\frac{a}{1-i} ; z_{2}=\frac{b}{2+i} ; z_{3}=a-b i \text { for } a, b \in R
\]
if \( z_{1}-z_{2}=1 \) then find the centroid of the triangle formed by the points \( z_{1}, z_{2}, z_{3} \) in the argands plane
(a) \( \frac{1-7 i}{9} \)
(b) \( \frac{1+7 i}{3} \)
(c) \( \frac{i+7}{9} \)
(d) \( \frac{1+7 i}{9} \)
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