In space,the equation $by + cz + d = 0$ represents a plane perpendicular to the

The equation of a plane passing through $(-1, 2, 3)$ and whose normal makes equal angles with the coordinate axes is

If the image of the point $A(1, 1, 1)$ with respect to the plane $4x + 2y + 4z + 1 = 0$ is $B(\alpha, \beta, \gamma)$,then $\alpha + \beta + \gamma =$

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

$A$ variable plane at a constant distance $p$ from the origin meets the coordinate axes at $A, B, C$. Through these points,planes are drawn parallel to the coordinate planes. The locus of the point of intersection is

The volume (in cubic units) of the tetrahedron bounded by the plane $3x + 4y - 5z = 60$ and the three coordinate planes is