CUET Mathematics 2025 14 May Shift 1 PYQs

The shortest distance between the following lines:

$\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + s(2\hat{i} + \hat{j} + \hat{k})$

$\vec{r} = (\hat{i} + \hat{j} + 2\hat{k}) + t(4\hat{i} + 2\hat{j} + 2\hat{k})$, where s and t are scalars, is:

The foot of the perpendicular drawn from the point $(1,6,3)$ to the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ 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: