The equation $xy = 0$ in three-dimensional space represents

The equation of the plane,passing through the midpoint of the line segment joining the points $P(1, 2, 5)$ and $Q(3, 4, 3)$ and perpendicular to it,is

The angle between the planes $3x - 4y + 5z = 0$ and $2x - y - 2z = 5$ is

If the plane $\frac{x}{3}+\frac{y}{2}-\frac{z}{4}=1$ cuts the coordinate axes at points $A, B$,and $C$,then the area of the triangle $ABC$ is

$\vec{n}$ is a unit vector normal to the plane $\pi$ containing the vectors $\hat{i}+3 \hat{k}$ and $2 \hat{i}+\hat{j}-\hat{k}$. If this plane $\pi$ passes through the point $(-3,7,1)$ and $p$ is the perpendicular distance from the origin to this plane $\pi$,then $\sqrt{p^2+5}=$

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