(a) The scalar product of the vector $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ with a unit vector along sum of vectors $\vec{b} = 2\hat{i} - 4\hat{j} + 5\hat{k}$ and $\vec{c} = \lambda\hat{i} - 2\hat{j} - 3\hat{k}$ is equal to $1$. Find the value of $\lambda$. OR (b) Find the shortest distance between the lines : $$\vec{r} = $2\hat{i} - \hat{j} + 3\hat{k}$ + \lambda$\hat{i} - 2\hat{j} + 3\hat{k}$$$ $$\vec{r} = $\hat{i} + 4\hat{k}$ + \mu$3\hat{i} - 6\hat{j} + 9\hat{k}$$$