question_answer

If the lines \[\vec{r}=-\hat{i}+\hat{j}-\hat{k}+\lambda (2\hat{i}+\hat{j}+3\hat{k})\] and \[\vec{r}=-2\hat{i}+\alpha \hat{j}+\hat{k}+\mu (2\hat{i}+4\hat{k})\] \[(\lambda ,\,\mu \in R)\] are coplanar, then the value of \[\alpha \] is _____.

Answer:

7.5