The line \(\frac{x-1}{2}=\frac{y+2}{-1}=\frac{\mathrm{z}}{1}\) intersects the XY plane and the YZ plane at points \(A\) and \(B\) respectively. The equation of line through the points \(A\) and \(B\) is

1. A \([\bar{r}-(\hat{i}-2 \hat{j}+0 \hat{k})] \times\left(-\hat{i}+\frac{1}{2} \hat{j}-\frac{1}{2} \hat{k}\right)=\overline{0}\)
2. B \([\overline{\mathrm{r}}+(\hat{i}-2 \hat{j}+0 \hat{\mathrm{k}})] \times\left(-\hat{i}+\frac{1}{2} \hat{j}+\frac{1}{2} \hat{k}\right)=\overline{0}\)
3. C \(\overline{\mathrm{r}}=(-\hat{i}-2 \hat{j}+0 \hat{k})+\lambda\left(-\hat{i}+\frac{1}{2} \hat{j}-\frac{1}{2} \hat{k}\right)\)
4. D \(\overline{\mathrm{r}}=(\hat{i}+2 \hat{j})+\lambda\left(-\hat{i}+\frac{1}{2} \hat{j}-\frac{1}{2} \hat{k}\right)\)