Three Dimensional Geometry

$[\overline{\mathrm{r}}-(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+0 \hat{\mathrm{k}})] \times\left(-\hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}-\frac{1}{2} \hat{\mathrm{k}}\right)=\overline{0}$

$[\overline{\mathrm{r}}+(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+0 \hat{\mathrm{k}})] \times\left(-\hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}+\frac{1}{2} \hat{\mathrm{k}}\right)=\overline{0}$

$\overline{\mathrm{r}}=(-\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+0 \hat{\mathrm{k}})+\lambda\left(-\hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}-\frac{1}{2} \hat{\mathrm{k}}\right)$

$\quad \overline{\mathrm{r}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}})+\lambda\left(-\hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}-\frac{1}{2} \hat{\mathrm{k}}\right)$