CUET Mathematics 2025 15 May Shift 1 PYQs

The angle between the lines

$l_1: \frac{x + 1}{1} = \frac{2 - y}{2} = \frac{z - 1}{1}$ and $l_2: \frac{x - 1}{4} = \frac{2y - 4}{6} = \frac{z - 1}{2}$ is

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

A line passes through the point with position vector $3\hat{j} - \hat{i} + 4\hat{k}$ and is in the direction of the vector $\hat{i} + \hat{j} - 3\hat{k}$. The equation of the line in Cartesian form is: