CUET Mathematics 2025 15 May Shift 2 PYQs

Let the equation of lines be as $L_1: \vec{r} = \vec{a_1} + \lambda\vec{b_1}$ and $L_2: \vec{r} = \vec{a_2} + \lambda\vec{b_2}$ such that $\vec{d_1} - \vec{d_2} = 2\hat{i} + 4\hat{j} + 4\hat{k}$ and $\vec{b_1} \times \vec{b_2} = 8\hat{i} - 4\hat{k}$. Then the shortest distance between $L_1$ and $L_2$ is

The coordinates of the image of the point P (5, 4, 2) in the line $\vec{r} = (-\hat{i} + 3\hat{j} + \hat{k}) + \mu(2\hat{i} + \hat{j} - \hat{k})$, where $\mu$ is a parameter, is

If the lengths of the three sides of a trapezium other than the base are $10 \mathrm{~cm}$ each, then the maximum area of the trapezium is: