Three Dimensional Geometry

$\mathbf{r}=(2 \hat{\mathbf{i}}-\hat{\mathbf{j}})+t(\hat{\mathbf{j}}+4 \hat{\mathbf{k}})$

$\mathbf{r}=(1+t) \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 t \hat{\mathbf{k}}$

$\mathbf{r}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+t(\hat{\mathbf{i}}+3 \hat{\mathbf{j}})$

$\mathbf{r}=(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})+t(2 \hat{\mathbf{i}}-\hat{\mathbf{j}})$