$\Pi_1, \Pi_2, \Pi_3$ are three planes which are respectively parallel to the $Y Z, Z X$ and $X Y$ planes at distances $a, b$ and $c$ forming a rectangular parallelopiped. $d_1$ is a diagonal of the face of $X Y$-plane not passing through the origin and $d_2$ is a diagonal of the plane $\Pi_2$ coterminous with $d_1$. If none of the coordinates of the vertices of the parallelopiped are negative, then the angle between $d_1$ and $d_2$ is

The obtuse angle between the lines whose direction ratios are determined by the equations $a+b+c=0$, $2 a b+2 a c-b c=0$ is

A plane meets the coordinate axes at $A, B, C$ respectively such that the centroid of the $\triangle A B C$ is $(2,3,5)$. Then, the equation of that plane is

Let $[x]$ denote the greatest integer less than or equal to $x$ and $k \geq 2$ be an integer. Then

$$ \mathop {Lt}\limits_{x \to k} \frac{\sin \left(2 \pi\left([x]-\left[\frac{x}{k}\right]\right)-x\right)+\sin k}{x-k}= $$