\(\vec{B}=\frac{\mu_0}{4 \pi} \frac{\times \vec{r}}{r^3}\) for \(B_1 \;\;\vec{r}=(-\hat{i}-\hat{j})\)

\(\therefore \vec{B}_1=\frac{\mu_0}{4 \pi} \frac{i}{2 \sqrt{2}} \hat{k} \times(-\hat{i}-\hat{j}) \ldots .(1)\)

for \(B_2\;\; \vec{r}=\hat{i}+\hat{j}\)

\(\vec{B}_2=\frac{\mu_0}{4 \pi} \frac{i \hat{k} \times(\hat{i}+\hat{j})}{2 \sqrt{2}} \ldots \ldots(2)\)

from (1) and (2)

\(\vec{B}_t=-\vec{B}_2\) and \(\left|\vec{B}_1\right|=\left|\vec{B}_2\right|\)