Answer
$\frac{R}{9}$
Work Step by Step
We know that the total length L of the wire is directly proportional to the resistance . Since it is given that the wire is cut into three segments of equal length, each segment has resistance $\frac{R}{3}$
Now the equivalent resistance of the wire segments connected in parallel is given as
$R_{eq}=(\frac{3}{R}+\frac{3}{R}+\frac{3}{R})^{-1}$
$R_{eq}=(\frac{9}{R})^{-1}$
$R_{eq}=\frac{R}{9}$
