The Cartesian equation of the plane passing through the point $A(7,8,6)$ and parallel to the $XY$ plane is

The vertices of a tetrahedron are $O(0, 0, 0)$,$A(1, 2, 1)$,$B(2, 1, 3)$,and $C(-1, 1, 2)$. Find the angle between the faces $OAB$ and $ABC$.

$A$ plane passes through the point $(1, -2, 1)$ and is perpendicular to the two planes $2x - 2y + z = 0$ and $x - y + 2z = 4$. Find the distance of the plane from the point $(1, 2, 2)$.

Find the Cartesian equation of the following plane: $\vec{r} \cdot (2\hat{i} + 3\hat{j} - 4\hat{k}) = 1$

Find the equation of the plane passing through the point $(2, 3, 1)$ and perpendicular to the line $\frac{x - 1}{1} = \frac{y - 2}{-1} = \frac{z + 1}{2}$.

If $(3,4,-7)$ is the foot of the perpendicular drawn from the point $(-2,3,6)$ to the plane $\pi$,then the sum of the intercepts made by the plane $\pi$ on the $X$ and $Y$-axes is