The perpendicular distance from the origin to the plane containing the points $(1, -2, 1), (2, -1, -3)$ and $(0, 1, 5)$ is...(in units)

If $\alpha, \beta, \gamma$ are the direction angles of the line $x = 4z + 3$ and $y = 2 - 3z$, then the value of $\cos\alpha + \cos\beta + \cos\gamma$ is...

The shortest distance between the lines $\vec{r} = (4\hat{i} - \hat{j}) + \lambda(\hat{i} + 2\hat{j} - 3\hat{k})$ and $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(\hat{i} + 4\hat{j} - 5\hat{k})$ is...

Let $\vec{r} \cdot (3\hat{i} - 2\hat{j} + 7\hat{k}) = 32$ is the equation of a plane and the line having direction ratios $(5, b, 3)$ is parallel to the plane, then the value of b is...