CUET Mathematics 2026 18th May Shift 2 PYQs

The angle between the pair of lines given by $\vec{r} = \hat{i} + 2\hat{j} - 3\hat{k} + \lambda (\hat{i} - 2\hat{j} + 2\hat{k})$ and $\vec{r} = 5\hat{i} + \hat{j} + \hat{k} + \mu (3\hat{i} - 2\hat{j} + 6\hat{k})$ is

The sum of all the values of $\lambda$ for which the distance of the point P (2, 3, $\lambda$) from the plane $x + 2y - 2z = 9$ is 3 units, is

If $\vec{r} = \vec{a_1} + \lambda\vec{b_1}$ and $\vec{r} = \vec{a_2} + \mu\vec{b_2}$ are two skew lines such that $\vec{b_1} \times \vec{b_2} = 2\hat{i}+3\hat{j}+2\hat{k}$, $\vec{a_1} = \hat{i}+\hat{j}+\hat{k}$ and $\vec{a_2} = 2\hat{i}+3\hat{j}+\hat{k}$, then the shortest distance between the lines is