Three Dimensional Geometry

The following lines are

$$\begin{aligned} \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda^{\prime}(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}), \\ \text { and } \quad \mathbf{r} & =(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}) \end{aligned}$$