The coordinates of the point of intersection of the lines $\dfrac{x-3}{1} = \dfrac{y-5}{2} = \dfrac{z-1}{-1}$ and $\dfrac{x-4}{2} = \dfrac{y-2}{-1} = \dfrac{z-4}{2}$ are...

If the plane $2x + 3y + z = 6$ cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

The equation of the perpendicular line from the point $(2,-3,1)$ to the line $\dfrac{x + 1}{2} = \dfrac{y - 3}{3} = \dfrac{z + 2}{-1}$ is

The angle between the line $x - 1 = 2 - y = \dfrac{2z - 6}{4}$ and the plane $\vec{r} \cdot (2\hat{i} + \hat{j} + \hat{k}) = 10$ is