Solution :
$\overrightarrow{B}=\overrightarrow{B_{xy}} +\overrightarrow{B_{yz}}+\overrightarrow{B_{zx}}$
$\qquad=\bigg(\large\frac{\mu_0}{4 \pi}.\frac{I}{R} \frac{\pi}{2} $$\hat k \bigg)+\bigg(\large\frac{\mu_0}{4 \pi}.\frac{I}{R} \frac{\pi}{2} $$\hat i \bigg)+\bigg(\large\frac{\mu_0}{4 \pi}.\frac{I}{R} \frac{\pi}{2} $$\hat j \bigg)$
$\qquad= \large\frac{\mu_0}{4 \pi}.\frac{I}{R} \frac{\pi}{2} $$(\hat i +\hat j+\hat k)$
$\qquad= \large\frac{\mu_0}{8R}.$$(\hat i+\hat j+\hat k)$
Answer : $\frac{\mu_0}{8R} (\hat i +\hat j+ \hat k)$