CUET Mathematics 2026 19th May Shift 2 PYQs

The shortest distance between the lines $\vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} - \hat{j} + \hat{k})$ and $\vec{r} = 2\hat{i} + \hat{j} - \hat{k} + \mu(4\hat{i} - 2\hat{j} + 2\hat{k})$ is

If the straight lines $x = 1 + s$, $y = -3 - \lambda s$, $z = 1 + \lambda s$ and $x = \frac{t}{2}$, $y = 1 + t$, $z = 2 - t$ with parameters $s$ and $t$ respectively, are coplanar, then $\lambda$ is equal to :

Let $(\alpha, 0, \beta)$ be the coordinates of the point, which divides the line segment joining the points (1,2,-3) and (1,-1,-4) internally, then $(\alpha^2+\beta^2)$ equals: