If the plane $\bar{r} = (\lambda + \mu)\hat{i} + (2 + \mu)\hat{j} + (3\lambda + 2\mu)\hat{k}$, where $\lambda$ and $\mu$ are parameters, intersects coordinate axes at points $(a, 0, 0)$, $(0, b, 0)$ and $(0, 0, c)$ then $a + b + c = $...

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 maximum value of $Z = 4x + 5y$, subject to the constraints $3x + y \leq 15, 3x + 4y \leq 24, x \geq 0, y \geq 0$ is